I agree, a 12 gauge is the way to go. I load 1oz at 1200 FPS for Trap and I can shoot at least 10 rounds before the recoil wears me out.
Whatever autoloader you get, don't get a kinetic gun, they have more recoil than a gas operated gun. I've shot both and its easy to tell the difference. My trap league is about 150 strong, and at least 30 are women, with another 30 juniors, so we've got plenty of recoil sensitive folks and only the youngest shoot 20 gauge. I believe the 20 kicks worse, because the guns are so much lighter. The 28 gauge is the way to go for the recoil shy.