For buttons, 24 or 26 gauge wire is fine. I use solid core (not stranded). You'll likely want to get some crimp on female spade plugs (for plugging onto the male tabs on the buttons), but some folks like soldering instead.
Note sure where you're located, but Frys, radioshack, etc will have it.
If you look, make of the home improvement shops (Home depot, Lowes) etc will too, and usually cheaper because they sell bigger spools of it.
I believe knievel said he found "doorbell wire" at home depot that was cheap and solid core.
You may want to pick up a few different colors, or at least black and "something" so you can keep the hot sides easily separated from the ground sides.