Congrats, I shot my first clay at the age of 6 and am still shooting them 28 years later.
Here's to many many more shoots for you and your family.
I think with lighter loads a 12ga is about the same as a 20 but most 20's are lighter and your son might handle a 20 better.
I would go for the 12 if he can handle the weight. You can always load down with the 12. The 12 will provide more versatility than a 20.
As for a recomendation, an autoloader would serve to absorb some of the recoil. Remington and Beretta make fine auto's. Beretta makes a youth model with a shorter length of pull. I'm sot sure about Remington making a youth model.
I would also load up some 7/8 oz loads for the mild recoil.