First off, unless we are talking about trap and clay guns where overboring comes into play, the brand of the gun is not going to make as much difference in recoil as the ammunition you feed it.

While there are a few loads (heavy buckshot, slugs, and turkey-3" and 3-1/2") that can really kick you, most of what you should be concentrating on for squirrels...2-3/4" #6's or #7-1/2's... should be of little discomfort when shooting. If you can comfortably handle the "low brass" loads, you should be able to move up to the magnum loads (deer, turkey, ducks, and geese) with a certain tolerance.

I would recommend that if you have little experience with firearms, you should start with a .22. I know, a lot of people are going to say "rifles and shotguns are totally different, or it isn't the same kind of practice, etc., etc." but I still say it will be beneficial. If nothing else, it will at least start you on the path that muzzle blast and report (however little) will not hurt you and it teaches you not to associate shooting with pain.

Lastly, if you find a 12ga. to be too much, but still want a shotgun, try one of the smaller bores like the 16 or 20. Both are still capable of harvesting deer with the right load and each are more than enough for squirrels and rabbits.