I bought each of my boys a new shotgun when they turned 10. One chose a Mossberg and one a Winchester, both 20 ga pumps, both youth models (short stocks). I required they choose a pump for their first gun. The Winchester came with a discount coupon for a full-length stock, which went on when that boy was big enough. Both guns gave good service. I borrowed a youth model Rem 1100 for the one who also wanted to try skeet.
Be warned that what you're starting may continue. My other deal with my boys was their choice of a new shotgun or deer rifle at age 16. One picked a 700 .30-06, the other a Benelli Montefeltro. Oh, I forgot the .22 rifles that came somewhere in there. And the Ruger .243 for my daughter when she asked about deer hunting.
Hope you are as fortunate I have been with my kids and shooting.