AeroGav

Nothing ready made that fits those requirements - they are pretty specific.
Perhaps you can get help with converting an airplane to a seaplane ?  I've only built two,  going the hydrofoil approach.   I manage to take off from water with TWR of 0.7,  but perhaps better hydrofoil design can get than down - or just use plain floats?       On LAythe of course, with less gravity, perhaps it is easier. 
https://kerbalx.com/AeroGav/Puffin
...the Kerlew hasn't flown in recent KSP - https://kerbalx.com/AeroGav/K133--Curlew
The trouble with hydrofoils is that there is no info in the editor about lift and drag in water,  it is pure trial and error.

In answer to your original question, the Pre-Cooler is outstanding at low speed and good enough at high speed to feed a single RAPIER all the way to mach 6.     The Shock Cone is outstanding at high speed (one can feed many) and ok at low speed (enough for one engine).    A combo of a single shock cone and single pre cooler could feed 6-8 engines across the speed range i'd bet.   However,  i always find i've got enough 1.25m nodes to cap off at the front that I'm running more intakes per engine than that.    Intake drag is pretty minor compared to fuselage drag now.
 
Re:  Your ship
1.   The best LF/Oxidizer tanks on a capacity/drag basis are the 2.5m ones.     Mk2 tanks are the worst, swap them all for Rockomax tanks then see if you can get away with less engines - exchange the quad mounts for triples.
2.   Engines are heavy.  RAPIERS 2 tons each,  they are hurting your Delta V massively.    A reasonably slick ship should be able to do fine with 30 tons per jet engine.         Or,  try one panther and one RAPIER per 50-60 tons.    The hard bit is getting past mach 1.  The Panthers can help there and are very light, by the time they quit at mach 3,  the RAPIERs will be going ramjet mode crazy.    If you can bust mach 1 you can bust 1400 m/s in level flight at 21km.     More RAPIERs than that doesn't get much more air breathing speed as their thrust falls off rapidly after mach 4.5,  it just kills your delta V with dry mass.     
3.  If you can angle your wings up where they attach the fuselage,  you can make sufficient lift with the airplane flying on prograde hold.   This keeps the fuselage angle to the airflow minimal and really cuts down on drag, which means less engines still.
4.  Wings that don't have fuel in them are a waste.      I only use non fuel wing parts if i need to change the position of CoL  without adding fuel to that part of the ship.
As for how efficient you can go,  well,  i did build this, which can orbit an orange tank.   The minimalist fuselage makes little drag on prograde, but the wings still make plenty of lift, so it doesn't need oxidizer and can get to space with the feeble thrust of a few nervs.     Those nervs in turn, sip fuel and get all they need from the wing tanks.
https://kerbalx.com/AeroGav/Andromeda


That said,  cargo bays add huge drag and have quite a bit of mass even when empty.   This thing will never be as efficient as a dedicated crew/science mk1 fuselage explorer ship.

Glad to see you're making progress.    
For incidence angle,  I'd go for 5 degrees rather than 2 -   5 is the optimum angle of attack for lift at supersonic & hypersonic speed, so that's what we care about.   Rather than fly the plane with SAS on Stability assist mode, you can then try flying with it set to Prograde Hold.   This will significantly reduce drag.  
Note, you've added incidence to main wing and the canards,  but not the strakes inbetween.   The strakes will therefore stall last, and being in front of CoM,  will keep making lift when everything else has quit,  and send you nosing up into a deep stall.     Remember kids,  stuff in front of CoM should have same or slightly more incidence than stuff behind it  .    If this makes her adopt too much of a nose up attitude in "hands off" flight,  move the wings back a bit !
What's your flight profile?    Top speed on the Panther will be in level flight at about 14km up.    You should be doing at least 750 before starting rocket,  though after 750m/s power falls away very fast.      If you can't keep your AoA down while doing that speed at that altitude, you deffo need more wing.  Ideally you should have enough wing to do that altitude on prograde , with only the lift from wing incidence.
Your screenshots are tiny but it looks like you were getting lift to drag ratio of about 1.6 to 1 in the middle picture.  That's horrible !     My "Stretch Ray" was getting  4.2 to 1 at 19km and 830m/s.   AoA is mostly to blame.
Can you put those solar panels in the cargo bay?   You're only going to need them once you're in space, keep em out of the wind till then.  Attach them to a cylindrical thingy within the bay, maybe your science junior.   Likewise, you could stick it on the side of the science junior within the bay.
Engine Nacelle intakes - minor thing, but it doesn't need that much intake area if you already got two circular intakes.   A single mk1 liquid fuel fuselage on the back of the main fuselage would hold just as much fuel for less drag.
MK1 rocket fuel fuselage short - behind the cargo bay.    Like i stressed in my space plane guide,  don't use mk2 parts unless you really need their unique capabilities.   An ft-400 tank holds the same amount of rocket fuel for about a third as much drag.

All of these parts hold 800 units of LF/Oxidizer
Compare the drag values however - 
Mark One FT800 tank - 1.40kn
Mk1 to Mk2 Adapter (long) - 1.93kn
Mk2 Rocket Fuel Fusealge (long) - 2.36kn
2.5M to Mk2 Adapter - 2.44kn
2.5M Rockomax X200-8 Tank   -  0.47kn
 

The best way to determine if a part is shielded or not is to press ALT + F12,  go to the Physics Tab,  check the "Show Aero Data in Action Menus" tickbox.
Right click on the part while your craft spawns on the runway,  and  get into a high speed taxy.  
The right click menu will show "Shielded True:False".   Since the 1.3 update I've found it hardly ever shows "Shielded : True",  yet the part can have zero drag.   So the drag value is what the OP should be paying attention to, especially given that's his reason for using the cargo bay.
Re:entry heat is harder to test.   You'd have to use the "Set orbit" cheat then get it re-entering to be certain.    I've found that the game is more lenient with heating than drag however.   
Parts which are attached inside a cargo bay, but offset outside of them (custom cockpits for 2.5m spaceplanes) get drag, but seldom have heat.
 
 

From what I remember,  all 3 of the axial intakes (engine nacelle, diverterless intake, pre-cooler) have very similar drag value - about equal to a mk1 liquid fuel tank.    
@bewing said, different intakes have different air gathering performance.   Some intakes have a very high "static" rating,  and pull in a lot of air even when the craft isn't moving.    As speed increases, all intakes are able to gather more air, but eventually they reach a peak and beyond this, they take in less air the faster you go.    High speed intakes tend to have a worse static rating, but gain more rapidly as speed rises and hit their peak flow at higher speeds.
Most jet engines also increase in thrust (and air consumption) as speed rises,  and have a similar peak after which thrust and air use goes back down.
So,  it's important to match the characteristics of your intake with your engine.    
The Panther engine peaks at Mach 2.5 and stops producing power altogether at mach 3, so it will do fine on any intake.   However, I've had problems running a RAPIER on the supersonic radial intakes.   The air flow drops to zero above mach 3.5, right when the RAPIER gets into its peak,  so you'll get spluttering no matter how many you spam.
The Shock Cone is the most high speed optimised intake.  At high speeds, one shock cone can feed multiple rapiers, (but you might get spluttering at low speed with less than one intake per engine).  
The Adjustable Ramp and Pre-Cooler are not quite so high speed, but are well balanced enough to work with any engine on a one engine per intake basis.   The pre-cooler in particular has a high static rating despite being a high speed design, but on the other hand doesn't hold much fuel.
If you want to test this out for yourself, build a plane with multiple intake types , enable the drag data in the ALT F12 menu,  and fly around with the right click menus pinned in place, taking screenies.
Not moving - 
1. Engine Nacelle wins, flowing 18.9
2. Pre Cooler  flows 12.2
3.  Diverterless flows 6.8
4.  Shock Cone only does 4.5

Low Speed - 
Shock cone only has 60% of the drag of the others, which are all the same 0.90kn of drag. Looks like it's drag got reduced in the last patch.
1. Shock Cone pulls in 96 units of air
2. Engine nacelle pulls in 80
3. Supersonic intake does 77
4. Pre cooler does 68

Mach 2.65  (top speed for Panther, pretty much)
At supersonic, the engine nacelle and supersonic intakes are still the same for drag, but the pre-cooler has about 30% less and the shock cone 30% less again.
Shock cone pulls 31 units
Pre-cooler jumps to second place, with 18.9
Supersonic intake pulls 18.7u
Engine Nacelle falls behind the pack, with just 8u

 

First thing, it looks like you got 3 size 1 liquid fuel tanks - 1200 units of liquid fuel.   That's a huge amount, unless you really need to circumnavigate 3 times without refuelling all that does is drive up your takeoff and landing speeds.
Second,  those basic swept wings are unique in that their lift rating is half what it should be for their mass.     All other wings have the same lift:mass ratio, and BTW drag is based on lift rating, mach number, air density, and angle of attack, not shape.    So basically , don't use those wings .   Cobble together something out of the basic square and rectangular slabs you also get with the  basic aviation tech.  Those crappy  swept wings are forcing up your takeoff and landing speed by their poor lift.  
Third,  in KSP most drag comes from fuselage parts, and what really creates huge drag is when you join parts together with non-matching attachment node diameters.
So
 your cockpit (1.25m node) appears to be joined to a 0.625m probe core - this creates drag due to size mismatch  the 0.625m probe core (0.625m node) then joins to a mk1 fuselage with a 1.25m node - another size mismatch drag problem at the back, it looks like the fuselage ends abruptly - a 1.25m attach node with nothing on it, creating huge "flat plate" drag.   Needs a tail cone or nose cone to cover its back end offsetting/clipping stuff doesn't affect drag, (it only moves the point where the aero forces act on your ship) The best fuselage design for a starter plane like this is to put a 1.25m service bay behind the cockpit (stick your 0.625m probe cores and lumpy stuff here out of the wind) then go to a tail cone connector.      You have generally the right idea clustering size 0 engine nacelles around the main fuselage or hanging off the wing .  Just make sure the arrangement is symmetrical - i hope you've got more than 2 engines in that picture because the two i can see are above centre of mass.    They will tend to pitch the nose down when you throttle up, which could make it tricky to fly.

Youtubers (*staple vegetable high in antioxidants)
SAS in the default "stability assist" setting makes things very jerky, especially if you are flying on keyboard.
It remembers the nose attitude you had the last time you touched the controls,and tries to maintain that.   Every time you apply an input, this resets.  SAS might be holding the nose up at a 10 degree AoA,  but if you touch the rudder to remove a 5 degree sideslip this resets everything and the nose falls to 0 degrees AoA,  the plane stops generating lift and goes into freefall.
Problems with SAS -
pitch - SAS tries to maintain the same nose attitude with respect to Kerbol, the sun, rather than the planet you are flying around.  This means the nose slowly rises as you go around the planet , the aircraft will eventually stall if you don't correct this. Heading - Again, absolute heading is what it tries to maintain.  If you are north of the equator this will change as the north pole moves relative to you , even though the airplane is going in a straight line.   SAS tries to maintain the same absolute heading by feeding in more and more rudder correction, sideslipping the plane. Roll - If the wings are not perfectly level the aircraft will slowly turn,  SAS tries to correct this by feeding in rudder (generating sideslip, which then tends to induce more roll) rather than by removing the roll that's generating the turn in the first place. Youtubers   are probably making a video to demonstrate an impressive payload mass fraction or interplanetary delta V,  so their craft will not have the luxury of excessive thrust to weight.  As such they need  to be able to adjust pitch angle in 2 or 3 degree increments.
I fly low TWR spaceplanes on keyboard, i use one of two strategies to control pitch accurately - 
1.  For airplanes with non-angled wings, i turn SAS off completely in the  atmosphere and just use pitch trim (ALT S + ALT W) to control climb rate.  
You can see that during the speedrun i am feeding in nose-down trim to stop the plane climbing.   When we max out, i add several notches of nose up (alt + s) until we have an angle of attack of 5 degrees, which gives best supersonic lift drag ratio, and start the nukes.
2.  For airplanes with angled wings (built in incidence angle) I  do use SAS, but keep it locked in Prograde mode, because the wings still make lift even with the body at 0.
Note that Prograde does not maintain exactly 0 AoA in the atmosphere.   It feeds in a certain amount of nose up or nose down input to try get the plane closer to prograde,  but if the plane's aerodynamics would make it fly at 8 degrees nose up without input, then with prograde hold, this is error is reduced to maybe 2 degrees or so.      This can be used to your advantage,   this airplane uses trim flaps bound to action groups so you can adjust the nose angle a few degrees up or down from prograde -
https://kerbalx.com/AeroGav/Stretch-Ray
Note that when landing it though,  on keyboard,  I too used SAS with this aircraft.    The difference being i am not bothered about the drag created by jerky movements,  i just want it to respond quickly to corrections and hold a steady attitude when i'm not making corrections -
 

OK,  I tried a redesign of your vehicle keeping the above principles in mind and got this -
https://www.dropbox.com/s/f0n7zx03nhrn9e5/Laythe Lander.craft?dl=0

Similar mass, the only problem might be that it is longer.    Two aerospikes in the lower stage, one terrier in the upper and asparagus staged oscar b auxilliary fuel tanks.    Can get to orbit on kerbin with loads of delta v spare so it is total overkill for laythe.  Did not need fins because it is wider at the bottom than the top (more drag at bottom) but has most of the fuel mass at the top .

That effect is called Angle of Attack,  Lift and drag are both dependent on Angle of Attack (as well as mach number and air density).
At zero AoA , you get zero lift, but you still get some drag.
As  AoA rises,  lift increases rapidly at first, increasing faster than drag, until your best lift:drag ratio AoA is reached (about 5 degrees in supersonic flight).   After that, gains in lift slow down, and are outpaced by drag buildup.    At 30 degrees the wing stalls and lift gets less with increased pitch up, but drag still continues to increase.
> yes , in critical phases of flight you want to keep AoA under 5 degrees.
In steady state flight that means adding more wing area, or flying lower for a given airspeed.   In KSP you can cheat this a bit by adding incidence angle to your wings, since fuselage parts have nearly 10x the drag of wing parts.   This allows you to keep the fuselage at 0 while the wings are making lift at 5 AoA.
But if you're gonna do that  ,  make sure you add the same amount (or more) incidence to the front wings as to the rear ones.   That way, as you pitch up, the front wings start to stall first and gently limit max AoA.   Otherwise the main wings are the first to loose lift which will cause the nose to want to rise further at high AoA.
Incidence angle - easiest way to put it on your craft is to install Editor Extensions Redux.   It allows you to create custom angle snap angles for rotate part mode (instead of just 15 degree snaps).     so you can tell it to do 5 degree angle snaps, or whatever you like.
I also strongly recommend you install CorrectCoL mod if you're going to be getting into such advanced aerodynamic techniques.   The stock blue indicator only takes  account of aerodynamic forces from parts that have a "lift rating" in the part description, and cannot be trusted, especially on a craft like yours with more fuselage in front of the wing than behind it. 

If all else fails, alt f12  , cheats, hack gravity and use your jetpack to fly to the cockpit

Size isn't important 
I strongly recommend two mods to help you build stable aircraft  - RCS build aid,  and  CorrectCoL
RCS build aid shows a red ball in SPH which indicates where your CoM will be when empty.
You can do the same thing by manually emptying all the tanks but trust me ,  the number of times you need to check this when building a complex spaceplane, it saves much work.
CorrectCoL   makes the blue ball more accurate.     At the moment, the Blue ball only takes account of parts with a lift rating in their description.   But in reality all parts interact with the airflow and create forces.   You have a lot of fuselage in front of the CoM and it has a longer lever arm than the stuff at the back, it may be that your CoL is further forward than you think it is.
That layout you have there btw, has the cargo in front of the CoM, which means it's always going to be either a bit too nose heavy when laden or a bit too tail heavy (flip happy) when empty.   Best is cargo bay dead centre of CoM, with half your fuel right behind the cargo bay and half right in front, or on sponsons either side.     
 
CorrectCoL has a more sophisticated Static Analysis graph you can bring up too, for pitch and yaw.
The nuclear option for stability/flipping problems is to check and tweak incidence angles.      
Usually, surfaces are attached at zero incidence angle and all aero surfaces on the ship will have the same AoA.
If they differ however, it is imperative that surfaces ahead of CoM should have greater AoA than ones behind.     That way, wings at the front gain lift slower than wings at the back as AoA increases, as they get into diminishing returns (or even a stall) first.   However, because this increases lift on the front end at low AoA,  it moves the blue ball forward, so you need to slide the wings back a bit.
Short version -  Using fine rotate tool, rotate your front Canards up ever so slightly.    Rotate the elevons , on the trailing edge of the wing , down ever so slightly.    This will cause the blue ball to move forwards in SPH, so you'll need to slide the wings back to keep it behind CoM.  But it will now fight back if you try to stall it.    Its like being held to a railway line by a strong rubber band,  You can steer a few degrees either side of prograde but if you go too far it yanks you back in line. 

Thanks for the pictures.
First of all, mk2 fuselages are arguably bugged right now, they produce 4 times as much drag as a mk1 without actually holding any more fuel.
It would be much easier if you started off with a mk1 fuselage design,  just use an inline cockpit and put it a few modules back from the front so it doesn't get affected by the heat of high speed flight.  Inline cockpits are vastly less susceptible to heating - an inline mk1 will be less prone to blowing up the mk3 cockpit because it has to go at the front !
Second,   engines are heavy.  Rapiers are 2 tons each, Whiplashes weigh 1.8 tons, Aerospikes 1 ton.   Your vessel probably weighs 30 tons,  but is carrying 10 tons of engines.   Allowing for the structure and cockpit, cargo, it must have a fuel fraction under 40%?  That is why fuel runs out before orbit.
If you can reduce drag, you won't need as much engine.   Looking at your ship, i'd try to replace as many mk2 parts with mk1 fuel tanks as possible - if you insist on keeping it a mk2,  use them only for carrying kerbals and cargo.  Try to put nearly all your fuel in mk1 parts instead.  Also I'd recommend an inline cockpit even if you stay as a mk2.  Those rapiers can get up to 1600 air breathing in level flight at 22km - but if your cockpit is right at the front it will melt.
Profile - 

A good flight profile reduces the need for lots of engines.   Jet engines behave a lot like ramjets in this game, they produce more thrust at supersonic speeds.    But,  the air down low is really thick and draggy, which makes getting supersonic difficult, also the transonic region (mach 0.9 to mach 1.2) as more drag even than supersonic flight.     On the other hand, if you climb too high without speeding up, the air gets too thin for your wings.  You end up pulling the nose more than 5 degrees above prograde , which makes for high drag.
Here's my latest mk2 -
https://kerbalx.com/AeroGav/Penta-Shuttle


It's a not as nice looking as yours though :-(.
    1 Rapier at the back of the fuselage is enough to get it to 1400 or so air breathing.   But not enough to get through sound barrier, so it has 2 Panthers for an extra boost low down.  Once the Rapier is on song, it doesn't need them.   There's also 2 NERVs which can boost it to orbit all by themselves, and use up the considerable liquid fuel capacity of the wings.   As you can see, it can reach minmus very easily.
    

Have you tried re-entering the vehicle intact, but with the service bay open?
That way, you will have a high drag part, which is closer to the back than the front of the ship.  It might enable it to  stay retrograde long enough to shed a bit of speed.    If you have any fuel left, pump it all to the bottom tank (the one nearest the terrier engine).
This is why aviation tech is absolutely essential even if you're doing a rocket centric career.   Steerable fins would make it possible to keep the capsule facing whichever way you want.   The simple fixed fins you get before that are a death trap.  They let you keep the correct end pointing towards space on the way up, then turn your capsule into a lawn dart when you try re-enter.
 
 

CoL underneath CoM shouldn't affect pitch or yaw stability much, if at all, but it does make the plane less stable in roll - unless there's any dihedral to counteract this effect, the plane will have negative stability in roll, but I got the impression the OP was more concerned about pitch. 
@TeeGee I recommend downloading CorrectCoL  mod  , it updates the stock CoL indicator so it takes into account fuselage parts and not just wing parts.    You have a lot more fuselage in front of CoM than behind it, and fuselage does generate some lift, so it is possible CoL is not as far aft as you think it is.
Also I'd like to shout out to RCS build aid since it gives a nice red dot that shows where your CoM will be with empty fuel tanks.
BTW are you actually test flying it like this, since presumably it can't make orbit alone, and normally rides up with a load of solid boosters?
edit -  those Vector engines at the back weigh 12 tons.  You only have  a 4 ton cockpit at the front to balance them.   What happens when you empty the cargo bay, where does your CoM move to ?

I've not done Eve before - my rockets are only occasionally successful, due to dumb luck - i haven't developed the "feel" and "rules of thumb" to design them successfully in the way i managed with aircraft.
But someone mentioned drag being important.  In which case i suspect you want to use mainly 2.5m stacks, since i found these to have the best fuel capacity to drag ratio of any type of tank, by quite some distance.
 

It looks like you're using some modded engines there?
In terms of the stock engines,  Panther is no good if you want to go past 750 m/s,  it peaks there and thrust more or less falls to zero by 800.    It's going to be between the Whiplash and Rapier, which peak at 900 and 1150 respectively.    Looking at the atmosphere curves of these engines, thrust drops more slowly than air pressure up to 17km on the whiplash, then up to 22km on the Rapier.
Fuselage.   The mk2 fuselage has 3 times the drag of the mk1 but holds no more fuel.    It is more heat tolerant, but you 're using a mk1 cockpit.  Also parts at the front get the worst heat, if you were bothered about heat you could have just used a mk1 inline cockpit.   You can work around this problem, by adding an angle of incidence to your wings, but it's an "intermediate/advanced" technique.   Just stick to a mk1.
Wings - The big S wings and strakes should be used , they store additional liquid fuel.  You can build tail fins out of big S strakes too. 
For high speed with long range, you need to be flying at high altitude.  The higher the better, the lower your drag and fuel consumption.   But , you need sufficient wing area to cruise at your chosen cruising altitude with the nose 5 degrees or less above prograde.   If you are having to raise the nose more than this, you'll get excess drag.  
For getting through the sound barrier on an underpowered ship, what i do is climb subsonic (below 240) until the air gets too thin to support the plane without raising the nose more than 7 degrees above prograde.  Then i reduce the nose angle so it's only a degree or two above prograde, let the plane fall into a shallow dive, and start gently easing back up again above 440.
 
 

Use bigger wings ,  it will be easier to land.     
At the end he crashed because of high rate of descent.   Needs to be less than 5 m/s vertical speed on touchdown,  but  he could not get enough lift to stop the descent .     He cannot increase airspeed any more to get lift, because 80 m/s is already dangerously fast.
Why does his ship have bad lift?
His pitch controls are on the main wing, close to the centre of mass.
Those don't have much lift, and they can only get the nose up by pushing the tail down.   Because they are very close to the centre of mass, they have to push down very hard to make the nose go up - this negates most of their lift.
 
Replace those  with 
and use a proper control surface on the nose or tail -
 replace with 

Yes, it is because of SAS.
SAS maintains a constant nose angle relative to Kerbol (their sun), not taking into account the curvature of the planet you are flying over. If you add trim it will simply fight it, trying to keep the nose pointing where it thinks you should be pointed.
You can try flying with SAS off, but that requires a directionally stable aircraft, and that's something I struggle with despite having thousands  of hours in game, building almost nothing other than aircraft and spaceplanes.  Some say this is due to a bug in the physics engine causing phantom rolling moment.
Conventional aerodynamic wisdom says the following things help a plane fly straight
Wing Dihedral Lots of yaw stability, ie. generously sized vertical stab placed as far behind CG as practical High wing design, ie. wing above CG Whilst these guidelines help, building a stable aircraft is still very hit-or-miss.

Despite having all three of the above qualities and a low part count, it slowly rolls left with SAS off.
OTOH , this thing can be trimmed to fly hands off 40km up, despite smaller stabilizer area relative to weight, lower mounted wing, less pronounced dihedral and more doohickeys hanging off it than a Christmas tree.
I'd say you've got three choices
  Download a better autopilot mod   Just don't accept these survey contracts unless they within 5 minutes flying time of KSC.    I play airplane/spaceplane-only career games and i still won't touch them.   They are just not time efficient.  Spend an hour flying to the other side of Kerbin, an hour back, correcting the plane's flight the whole way, for a very small amount of cash?   Or do it with rockets, ok that's a minimum of three rockets (which must have v. close to orbital delta v) assuming your re-entry trajectory is perfect every time,  and get basically zero recovery value on them due to landing on the wrong side of the planet. build a plane that can fly on prograde assist. Because prograde assist tries to hold zero AoA you need to angle the wings upward when attaching them to the fuselage in order to get any lift.   If your plane is a canard,  you must angle the canards upward by at least the same amount so that the canards stall before the main wing.   All of this will radically reposition your CoL indicators, so you'll have to slide the wings aft a bit to get the blue ball behind yellow again.  Finally, you'll want to make further small adjustments to the angle of the canard or tailplane until the plane flies at small positive aoa hands off and untrimmed.
Prograde assist does not attempt to correct roll but will try to dial out any yaw, so provided you got roll stability with dihedral it should want to keep the blue side up.
At  low altitudes, you prograde plane may drive you crazy with loop-the-loop antics since it'll generate too much lift when you bang the throttle open.   However,  as they get near their max altitude they calm right down and cruise pretty nice.
https://kerbalx.com/AeroGav/Bute-Ranger

This career mode plane can supercruise economically at high altitude with only occasional roll corrections in time warp.  Almost makes survey contracts worthwhile - but not quite.
 

I don't know if you're making a replica of the whole dreamchaser stack or just the orbiter.
If you're only bothered about the orbiter looking right,  might it be easier to radially attach four smaller boosters around the orbiter, so the lift from the orbiter's wings is near the bottom rather than the top?
Otherwise you need to put giant wings on the very bottom of the booster to try and balance the lift coming from the spaceplane.

Unmodified.
I took off, had a look at how much nose up input SAS was using to keep it level.  Turned off SAS  and used pitch trim ALT + S, to trim the nose up to the same point - about 5 degrees above the horizon.  Let it climb to about 5km, by which point we're getting near 250m/s - time to go supersonic.  Reduced the nose up trim with ALT + W so the nose is only 2 or 3 degrees above prograde.  Kept trimming it down more as the speed built up to stop it trying to pull up prematurely.   At 440 m/s , I get it climbing again.      Around 13 or 14km I notice we're going to zoom out of the atmosphere prematurely, use prograde to gently level off.     After that i switch between prograde and SAS to keep the nose where i want it.
When heat bars appear, climb a bit.  When air gets too thin (over 21km) for it to accelerate much more, switch mode.    By this point we're doing over 1500m/s.  From this point on I maintain nose about 5 to 10 degrees above prograde.
There is only enough oxidizier to get us to about 1900 or so.    That's actually pretty well judged.   2 nukes are just - barely able to get us to orbital velocity from there before we start to fall back and burn up.
To make orbit, you have to get 1500 air breathing because oxidizer only adds another 400 velocity before running out.   And you need to be at 1900 when the oxidizer runs out or the 2 nukes are too weak to circularise.
By the way, the pointy mk2 cockpit nearly overheated.  An inline mk2 cockpit would do much better.

The action menu is the right click menu,  with this box enabled you get to see how much drag (and lift) each individual part is making.
By the way, when i started using these options my game started crashing lots.   To stop this, go into the graphics options off the main menu screen and turn off "highlight fx". 
AeroGUI
The wall of data looks intimidating at first, here's how i pick what i want from it -

 
Mach - this is useful because the engine thrust / speed curves are quoted in mach not m/s.  From the wiki

We can see that the RAPIER peaks at 3.75, still gives a good amount out to mach 4.3,  then starts to gimp out really quickly.  This chart shows why you should try to get mach 4.3 air breathing, but adding more engines to go even faster would be diminishing returns,
 
Pitch  /  Total Lift / Grav Force (Weight)
This data can help make your flying more accurate.  I mainly control pitch with trim controls on my designs (ALT S , ALT W) with SAS off.    Seeing that lift is less than weight, and that the pitch number is decreasing, gives you early warning to add more nose up trim, well before you'd notice it from just looking at the plane.  Note that in really steep climbs,  lift does not have to = weight, because engine thrust is directly pushing against gravity.  Also at very high speeds,  orbital effect is taking over and supporting more and more of your weight.
 
Aoa   and  Lift / Drag ratio
Taken together, they can help improve your flying.   They help me find the best nose angle during ascent.   Raise the nose slightly, your AoA goes up.  Has your lift/drag ratio gotten better or worse? What if i lower it instead.     On its own, the Lift/Drag ratio helps you see how efficient your design is.  At supersonic speeds,  2.5 is good in a mk2 or mk3 ship.  Mk1 can get over 3.  Last night i did build a mk3 that came in with a freakish number of 3.417.   Really underpowered ship so it's the only thing that gets her to orbit.
 
Total Drag vs Total Thrust
 
This is the big kahuna.  So long as thrust is the bigger of the two numbers, you can go to space today.  If it is not, then although you may be climbing (by bleeding off airspeed)  or getting faster (by shallow dive) you are in fact loosing energy with every second.

This is made worse because jet engines are much more powerful in KSP  than they are in real life.
To stop planes being too overpowered, they have reduced lift:drag ratios a lot compared with real life.
So,  you need more thrust to fly, but you have more thrust.  Which is fine until you have an engine out on one side, like you just discovered.
Also, the very powerful engines make it easier to simulate thrust reversers.   Just thrust backwards - done.
Real airplanes have lower thrust:weight ratios,  and thrust reversers don't redirect all of the airflow, nor send it straight back.
The air that does get redirected by the reverser, comes out mostly sideways and a little bit forwards.
This disrupts what is normally smooth airflow around the wing and engine to destroy lift and create huge drag.   It's like a "virtual parachute" .
They are very effective at landing speeds, but are normally turned off below 80 knots - by this point you're mainly just making noise - and trying to suck bits of gravel into the inlet.
 

Basic rules 
1.  Fuselage size - small diameter is best.
Stick with mark 1 fuselages if at all possible, they have so much less drag and weight.   If the ship becomes too long and bendy with mk1, and a shorter, fatter type 2 fuselage will fit the same number of kerbals, or if you absolutely need a mark 2 cargo bay, only then consider type 2+.
2.  Parallel fuselages - minimise frontal area
This is closely tied in to the number of engines you are going to support.   If you are building under 25 tons and are planning to use fuel and oxidizer, then you need only one engine (a RAPIER)  and it can be at the tail end of your only fuselage section.  No need for sponsons, engine pods, parallel fuselages or whatever to add frontal area.   
If, like me, you are building an oxidizer-free long range spaceplane that flies to orbit on a combination of air breathing engine and nuclear rocket,  you're basically forced to have at least 3 parallel fuselages - two for the LV-N strapped to the sides, one for the airbreather.
3.  Minimise radially attached  rubbish
Weight is easier to tolerate than drag.   Use reaction wheels insdead of thruster blocks, put stuff (solar panels)  in service bays if you can.  In line clamp o trons only.   Don't add more air intakes than you need. Avoid fuel ducts and struts, they are bugged and add horrific amounts of drag.
4.   Don't mount too many engines
One air breather per 30 tons is fine.    60KN of closed cycle thrust (one LV-N or one Terrier) is enough to put 15 tons in orbit.  Engines are very heavy and add substantially to your empty weight, they can quickly cut down your delta V.
5.  Don't be too stingy with wings
Look out for the ones that can double up as fuel tanks (big s strakes, big s shuttle delta wings, fat 455 airplane wing).   These are especially handy if you're making an oxidizer-free nuke/jet engine ship like mine since you need all the liquid fuel capacity you can get.
Above 20KM, air is very thin and if your wings are under sized you may need to use Angle of Attack > 10 degrees to get enough lift.  Over 10 degrees angle of attack drag goes up very quickly.  Matters less i guess if you have a very powerful oxidizer using rocket engine to get you past that awkward moment when you're no longer  a very good airplane but not yet a space ship.   On a nuke powered spaceplane however, it is important to keep drag down here so you can still accelerate with these weak engines, you also need to gain height at sufficient rate as you accelerate, to not overheat.  This all means plenty of wing.
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https://kerbalx.com/AeroGav/Astrojet-Citation
This is a 30 ton, one whiplash two NERV SSTO with the ability to take 5 kerbals and a docking port to Minmus.  Can also fly to Duna, land safely and go back to orbit again , but doesn't quite have enough for the transfer burn back to Kerbin unless refuelled.
Part one of my launch video.
 
The craft flies without any mods but Mechjeb makes it possible to fly climb angles accurate to within 1 degree , which saves a lot of effort and allows you to experiment with different profiles in a repeatable way.
Note how i've got mechjeb configured on the left.   Whatever i input in the "pitch" box is the AoA the autopilot will hold.   On the right aero data window, at the top of the third section,  see how closely AoA matches the "PIT" setting on Mechjeb . 
Six lines down you have "Total Drag" and "Lift Drag Ratio".  Throughout the flight i'm adjusting these to try keep Lift Drag Ratio as favourable as possible.    Four lines up from bottom, is "Thrust".  Notice how this compares with "Total Drag" as engines come on and offline, and move in and out of their sweet spots !
Edit - part two here, where we finally max out the little old airbreathing jet and light up the nukes.
 

The higher you go , the faster you can be without overheating.  Of course, as you get higher, the Rapiers will also lose power, so your top speed will be lower.  Looking at the config file, it seems the power really starts to fall off a cliff above mach 4.5,  so i generally aim for mach 3 to 3.7 at 20km, then try to be in a very shallow climb and accelerate to near mach 4.5.   After that I climb as high as possible without loosing speed.   When speed starts to decline, switch mode or if you 've got separate NERV engines or something, start those.
If you bring up the Alt f12 debug menu, go to Physics then Aero tabs, and check the "display aero forces gui" box , you get a nice set of stats including total drag and total thrust.  when you're no longer thrust-positive, time to go nuclear.