A single shot 410 or a 20 gauge would be just fine for a rabbit, and it wouldn't cost much more than $100 either. H&R makes some good single shot shotguns for like $120 new. On squirrels I only use .22 with subsonic ammo.
Thats what I have been using is the rossi .410...the thing is awesome and super light. In the state of Wisconsin it is illegal to use a .410 for deer hunting.