Go with a 28ga. Yes shells are a little harder to find but the recoil will be noticeably less than a 20. If you find a shotgun the fits you’ll be golden. I’ve clients that hunt pheasant and chukars with 28s, they have no trouble killing either of those. The guns are light as a feather, doubles that weigh five pounds and a little. If you put a 28 in a gas operated shotgun recoil will be negligible.
There really is a science to gun fitting. It does make a difference. That being said, next time you go to a gun store to look, with the gun balanced in your hands look down the wall at the far corner of the ceiling, or a mounted bird as far away as possible up to about 20 yards. Focus on the target close your eyes and mount the gun, open your shooting eye, if you’re on target without seeing too much of the rib you’re getting the idea of what good fit is.
Good luck