Gomiata,
Despite the fact we're on a double gun website, I'd vote for a 20 ga. auto as well. I'm blessed with covey of grandchildren, all nicely spaced about four years apart. I bought 2 Remington LT 20's, put a plastic youth stock on one, left the other with the original wood. I was lucky, one had an Imp. Cyl. fixed coke, the other a modified. Giving the little guys every possible opportunity for success, I barreled the youth gun with the I.C. I figure I'll be able to supply the covey for the next 15 years! My eldest grand daughter is 13, just about big enough to graduate to the full sized gun. Shooting 3/4 oz. #8 loads, these little autos have virtually no recoil and still break targets with amazing regularity. A real plus is a long plug making the youth gun a single shot, the kids are taught the action is either open and safe or closed and loaded. If you saw me shoot you'd know I shouldn't get into an arguement with anyone over the virtues of a single sighting plane vs. a s/s, but I believe it is easier to learn
An added benefit has been my daughter, who never took up shooting, has a ball shooting with her daughter! Whatever your decision, encourage those little guys to get out and try the shooting sports, our hobby needs an infusion of youth.