I started my 10 year old grandson off with a 22 and a 17 Hmr then we shot a few rounds of 243 and now he is shooting the rifle he'll use for elk - a 30-06.

Now it is loaded with 110 grain bullets and a minimum charge of powder so it kicks like a 243 with less muzzle blast but it is a 30-06 and by 12 he'll know that he can shoot his 06 better than most new hunters and by then he'll be shooting 180 grain TTSX full power loads.

There are tons of rifles and bullets that work for elk as will a 100 grain broad head going 200 FPS but my recommendation is 30-06 and 165 grain or bigger bullets.