Wire size: I like 20 - 22 ga for panels. Any bigger is probably overkill.
Stranded or Solid?
I have seen this debated so many times. The truth is that it really doesn't matter, unless you keep the machine in your RV and travel a lot. Solid core wire has been around a long time and if it was that prone to breakage, you wouldn't see it that much. As others have said, once it is in place, it's not going to be moved much, if at all, and that means no worries about breakage.
All of your house electrical wiring is solid core, as are most likely your network and telephone cables. Solid core has advantages in that you don't need to worry about short circuits when stuffing it into screw terminals and PCB holes for soldering, it seems to strip easier, it's more likely to stay where you bend it without as many mechanical supports, and so on.
There is one big disadvantage to solid core, however, and that is that most people prefer to use crimped connections to their controls. Crimp terminals aren't the best choice for solid core, as they can loosen and fail far easier than with the appropriate stranded wire.
Also, there is a cross out there of both types. I bought a bunch of it recently and it's pretty decent stuff. It's stranded wire with a tin overcoat. This gives it desirable properties of both types of wire and most importantly, it takes a crimp well. If you are unsure which type to use and you can find it, this type seems to be a good compromise.
RandyT