Ruger Mark series; get the bull barrel, really helps with accuracy. Plus, as cheap as they are, you can get two and several thousand rounds of ammo and still be a hundred bucks under budget, if not more.
Rugers, Browning Buckmarks, S&W 41's, or an original High Standard....all can exceed YOUR intrinsic accuracy. The most accurate .22's have sights that are fixed on the barrel; that is, they do not move with the slide during cycling.