So, you're probably going to hate this answer, but I think I'd put a red dot on a 22 target pistol, and use that. 100' isn't too far for that, and it would give you an excuse to get some shooting practice in.
If you're all set on a shotgun, I'd go 12 gauge, 1100 or 11-87, and 2-3/4" shells. I'm not a shotgun shooter either, on a couple of times, but know that the Remingtons are reliable and point well. As Half Fast and others point out, light loads in a 12 are probably less felt recoil the equivalent loads in a 20. And in my mind there's no reason for 3+" 12, unless you're hunting geese or something else high flying and large. It's a good point that you don't want to wound it, but I think that's WAY more likely to happen from poor shot placement than lack of power from the round.
Final thought....re-reading my last note and thinking about the miss problem, if you have a lot of land, maybe go .223 at keep a nice healthy 100+ yard distance from you. 22 rifle would probably be fine for that, too, at 100.
