I have a partscaster that I need to wire up.
I went to Radio Shack & bought some 24 gauge wire to use to connect the pots & 3-way switch.
Is that OK to use or do I need to use something special?
You may want to invest in some actual guitar wire (with the metal braid around the center core) just to make it easier, since you can carry the ground in the outer braid and cut the number of wires required in half. But that stuff'll work fine if that's what you have and you need to wire it up now.
Heck I once opened up a Strat to do some work, and there was a paper clip soldered across the back of the pots to ground them all. Worked fine, though I did remove it and wire them properly just out of principle.