Hi ScareCrow,
here are some handy advise:
1) Try to minimise payload (the actual spacecraft you want to send to other planets) this should be compact and small as can be.
2) Think of the building backwards: you build the spacecraft, then the tank with engine which it uses in deep space (small like the Pug or Terrier depends on size) then a larger tank and engine you will use to leave Kerbin SOI. Reliant, Swivel will do it. Don't build it too long though two medium size max. If you have External fuel pipes, you can put on 2-4 fuel boosters (rockets with engines) and feed the EFP to the centre. Finally you build a large lifter from the surface of Kerbin. Orange tank max twice. Maybe fuel boosters. Skipper or Mammuth engines. Then outside attach SRBs if you want. You need stabilisers for keep the whole thing in line. You can use Monopropellants too but consider their weight. Use fins and winglets to control them in the air.
3) Stages triple checked.
4) use struts to solidify. That helps especially in lower stages. Decouplers usually cause a lot of noodle effect. For example: when put on the SRB decoupler (side) is usually in the middle. Put at least one strut on the to and the bottom near the engine. Also connect the SRBs together for solidity.
4) Use cones on top of the boosters and fairings on the actual spacecraft. Winglets/fins on the bottom near the engine. Lifter stage should have a solid large one. No need to control while in the thickest atmo.
5) Learn how to asparagus fuelling. You can google it.
6) TWR! Figure out the stages TWR. Kerbal Engineer Redux (mod) is the best way to do it. If it is under 1 rocket won't lift, you waste fuel. Over 1.18 is good, higher the better. But! In atmo over 2 is actually create too much drag.
7) If the rocket start to spin you most likely did built something not aligned properly. Check the build. Use the tools in VAB to align everything.
8) You need around 4500 to leave Kerbin SOI, you have to have it without the Deep Space stage.
Hope these help.
God speed! Brave Kerbonaut!