A few things to consider - a semi-auto shotgun recoil is far less than a pump which is less than a single shot - so keep that in mind.
A 20 ga will do just fine at 40 if you pattern. My daughters used a Remington 1100 with 3" #4 copper shot with no problem at all. I even added a Tru-Glo sight to help them concentrate on the hit zone.
And we always tried to get the bird in at 20 yards or so as that is how I hunt.........
What a 12 does bring is more payload as far as number of shot per shell fired
........but a 20 will kill just as dead......
JW
I've always liked a semi even though alot of times I'll only load 1 shell.Just seems to feel better(to me anyways)