I started my son at 12 with a 30-06. I think its a good choice for a rifle as he can grow with it. If your boy is already shooting a 20 ga, even better start to centerfire. So, the load I started him out was 46grs H4895 and 150 Hornady RN. He had absoloutely no problem with it offhand!
For his first moose trip later that year we switched to a 150NPT. I would think a 130 gr load in a BAR would be even easier!!

Moosey