I use .22s and .22 handguns for squirrel. Shotguns are cheating. Even rifles seem like cheating. Rabbits, though, usually jump at your feet long before you see them and hitting one on the run is much easier with a quick pointing shotgun, though I have done it when there was enough room, time to get on 'em, with a .22 rifle. I don't know about hares (IE snowshoe), but I've killed cottontail with a rock, let alone a .22. They die easy. I do use a hollow point on 'em rather than the solids I shoot at squirrels and I'll shoot LRs only at rabbit where a CB short will kill a squirrel real dead.
Use an open choke in a 20 or 12. I've shot 'em with .410 and full choked of course and that is a pretty good choice, but now days I don't have a .410 and would use my little 20 gauge SxS and probably cylinder/IC choked. For squirrel hunting, I'd choke IC/Full, full for those long shots. 6-7.5 shot is appropriate and low brass AAs are fine. You don't need much for 'em.
If you're running rabbits with Beagles (big time fun), I'd advise choking a little tighter. I'd go IC/Mod with dogs. They can pop out of cover a little farther. If you're just walkin' round kickin' 'em out of cover, they're going to be right at your feet.