Getting my 9 yr old son into shooting, too. He’s quite a mean shot with a .177 air rifle but I want to graduate him into more tasty stuff.
Go for a lever .22lr rifle from Henry ... they have a youth model that is perfect until your son can handle a 13 inch length of pull. My grandson received one at age seven and is still using it at 13. I have a matching one I use and I’m 71! Great little lever gun, and with 60 grain Aquila bullets, a great home defense option.