As others have stated, I imagine it depends on what atmospheric depth you plan on hanging around at. Hot air balloons come in all sizes and shapes, thus I imagine that a rather "flat" balloon would be necessary for a base you would want to easily escape from. Depending on the strength of the wind, you might even want to have a balloons that act as "wings" of a sort for any extra lift you can scrape from the environment.
If your power source is nuclear of either the fusion or fission variety (which I assume it is if you're brave enough to build a floating base on a gas giant in the first place...), you could most likely dump the waste heat of your reaction into the balloon to keep you afloat. As Snark has pointed out above — your reactor would need to be either very efficient or very small or, preferably, both. Again, this is something I assume you'd have the technology worked out for before starting such a project in the first place.
Now actually getting OFF the base is a different story altogether. If your deep enough down, anything with high enough quantity of both lift and thrust should be enough to get you up and out with relative ease. If fusion is your powerplant of choice, starting out relatively empty on propellant and filling up your tanks as you ascend would be way to go. It would probably be significantly easier to do on a hydrogen rich gas giant than with a more "mundane" combined-cycle air-breathing rocket on Earth or Kerbin (i.e. SABRE).
The immediate example that comes to my mind as a potential ascent vehicle is the SSTO-TAV37B "Valkyrie" from Avatar(2009). When the ISV Venture Star arrives at Alpha Centauri A, it uses fusion engines as its means to transfer into a lower Delta-V orbit around Pandora. After the two Valkyrie shuttles that are docked to it finish transferring personnel and payload to Pandora itself, they dip into the gas giant Polyphemus' atmosphere to scoop fuel to return to the ISV itself to make ready for the return voyage to Earth. The delta-wing shape of the vehicle should also be sufficient in making use of whatever lift there is to gain at a reasonable "fuel scooping" depth in a gas giant's atmosphere.
As for the idea itself...well, I don't think its completely necessary to the KSP2 experience, but it is something I would like to see in one form or another. If anything, I would imagine that the better physics for planets overall — rather than just a thin crust of textures wrapped around an empty void — would provide the tools for modders to be able to add it in time. If there are easy to handle tools that control the ability to build bases (and it isn't just permanently and obtusely tied to us being forced to build them a specific way on-world or off-world), then I imagine it would be doable.
In terms of what we already know — we do know that orbital shipyards, terrestrial body base-building, fusion engines, torch engines and specialized fuel synthesis (at least for Metallic Hydrogen) will all be in the game, and we already have mining and LF synthesis mechanics in the base game in the form of the mining excavators and the Covert-O-Tron. We can safely assume that there will be more fuel types than just LF and LMH — with Methane, pure H2, and H2/Ox engines being the most likely (and already present in popular, expansive mods like Near Future Propulsion/Cryo). Since intakes already scoop air in-game, I would imagine it wouldn't be so far of a stretch to have specialized intakes for scooping gaseous hydrogen (for fuel) or helium (for fusion) from atmospheres rich in those elements.
Finally with allll of that said, I see two ways it could possibly go down:
1) The more likely way is that you can build an orbital shipyard, attach wings, a reactor, intakes, and engines to it either while building it or through grabbing units (if you can't build however you want), then slowly lower it into the atmosphere of say, Jool. You scoop fuel for both the engines and reactor with the intakes, stay airborne with the massive lift provided by the wings and the thrust of the engines, generate power to stay on heading with the reactor, and basically set it and forget it until you need to launch something from it. If your reactor generates enough power, maybe propellers would be something worth using instead or as a fallback, depending on the density at your desired altitude.
2) Orbital shipyards and base building in general doesn't let you attach random parts to the base structure itself, even with workarounds like grabbing units. Your best bet in this case is to build a giant platform with a few miniature spaceplanes/rockets, habitats, and modules docked to it instead. A lot less interesting and you won't be able to build stuff at that particular "base", but still doable as long as you have the right parts for the job.
Anyway, those are just my 99 cents.