if you are looking for a gun with some recoil/kick to it you aren't going to get a whole lot of that from any .22
If you want someone cheap as hell to shoot that can go through rounds quickly with moderate accuracy then you are looking in the right place.
Power: No, not really. Squirrels/birds are your best bet for game.
Fun: Yes. Even with increases in ammo prices 500rds 22 rounds are going to cost you nothing.