I am an NCSA instructor and coach a private schools youth shotgun team with our emphasis being on Sporting Clays. Unless the child doesnt have the upper body strength to handle a 7-8 lb shotgun, I try to get them in a 12 gauge as soon as possible.
The majority of our kids that are serious about the sport, and can afford it, end up shooting Beretta semi auto's. Mostly 391's , with a few 390's /3901's and A 400's in the mix. They are reliable with target loads, shoot soft, and are adjustable.
We also have a few shooting Browning Silvers, and SX2's and 3's. They are very good shotguns at a slightly lower price point than the Beretta's
In a used gun, there are a ton of gently used 1100's out there. Learn how to maintain it, what parts tend to wear out and fail, and it can be a reliable clay smashing machine.