Many on here will have more expert advice than me..........BUT...
With youth model guns most will outgrow them and they get relegated to the "memory" shelf and never used again. I started my son out with squirrel hunting with a .410 single shot shotgun. It was easy on his shoulder and he became used to it. We used .410 slugs in it for deer season (open sites) since I knew he had to limit shots to close range anyway and he already developed good sighting with squirrel hunting. (.410 has to be aimed more than pointed) He is grown now and uses a 30-06 but still has the .410 for occasional squirrel hunts and still gets use from it. At around 9-10 years old he went to 30-30 handloaded "light loads" (by a friend of mine), then 30-30 factory loads around 11-12, then went to 30-06 around 16. He never used a "youth model" and still uses the .410, 30-30 and 30-06. May not be the best method but it worked well for us.