I have a S&W Model 64 .357 - Stainless 4" heavy barrel; I gave it a light abrasive blast finish with polished cylinder flutes, latch button, trigger, hammer, and screw heads. Added a Wolff kit, and Pachmeyer grips. I get 6 rounds in 2" @ 25 yards offhand (if I do my part).
TheOverlord:
I usually recommend something like a Ruger Mk II .22 cal semi-auto, in either the Government or Target models. You can usually find them used for under $175 if you shop around.
They're very accurate, never wear out, cheap to shoot alot, and serve to easily teach the fundamentals of safe firearms handling and target shooting. If you get one, you'll probably never get rid of it, even if you decide you enjoy shooting enough to aquire other guns.
As an alternative, I would second Hamburgerpimp's choice of a .38 cal revolver. The one I mentioned above cost me $125 and needed a set of grips and some "clean-up". Since I was 'smithing on a regular basis at the time, and had already done similar treatments to two previous guns, I just turned it into a personal project for myself.