I'm a big fan of plain jane .22 lr. For small game its all you really need and there is a amazing variety of ammunition to choose from. If I was a serious varmint hunter then I'd look at the .17s but otherwise you probably want to preserve as much meat as possible on a rabbit or squirrel.

My fav sporting .22 is the Ruger 10/22. Very accurate and very reliable right out of the box plus it can be customized with a huge selection of aftermarket products. If your tastes lean toward the high-end the Kimber bolt actions are IMO opinion some of the most beautiful and accurate .22s made.

Finally, an accurate rifle really deserves some decent optics, even if its "only" a .22. If your .22 is capable of shooting 1/2" groups at 50 yards you simply can't take full advantage of that level of accuracy without a scope.