If you reload for the shotgun, there are an unlimited amount of recipes out there, from 3/4 oz going 1100 fps all the way up to 1 5/8 oz (in 2 3/4" 12 ga).
If you reload, I would look at a auto, in 12 ga, and reload the 3/4 oz loads for him to shoot single-shot. The stock can be cut down for his small frame (with care) and you can get a shorter barrel to also help reduce the weight. It would be easy to upsize the gun as he grew up without having to spend a lot of $$.
A big thing to help with recoil is make sure that the gun fits him, and get a nice soft recoil pad. Simms, Trap Dude, etc. make nice ones.
If you don't reload, then I'd look at a 20 ga auto, or try and find some of the cowboy reduced power loads for 12 ga.
Auto's will have the least perceived recoil, then Over/unders (bottom barrel), followed by pumps and single shots.
Just like a rifle, the "bullet" weight and speed vs. the weight of the gun determine the recoil. The cheap shtogun shells at the big box stores might recoil more than the premium shells even tho they usually have less shot in them due to the fact that they are usually going faster than the premium light target loads.
There are other options to help with recoil, but they run into considerable $$ (i.e. Soft-Touch or G-squared recoil reduction systems)
I probably will be saying something that you already know, but make sure that he wears ear plugs/ear muffs and preferrably both. I bought my nephew an inexpensive set of electronic ear muffs, and he wore them turned all the way up over a set of ear plugs. He still wears the muffs 5 years later.
I have a Franchi AL-20 that weighs 5# 3 oz, and it recoils about the same as my Remington 1100. (7/8 oz vs. 1 1/8 oz). I wouldn't recommend the .410 due to the difficulty of hitting clay birds with it.