I would pick any of the above in the original post.
OP handloads, means the loads can be adjusted from reduced to full power. Trailboss, H4895, starting, medium and full power powder charges. There are plenty of bullets that will work in the above cartridges at chosen velocity that will cleanly kill deer and antelope.
IMO, the most important thing is picking a rifle that fits, and the kid likes. Have them shoot it a bunch. Confidence and familiarity will lead to success.
Arguing about what a 22 cal is capable of, is not the point of this thread. But I will say that a 53gr TSX at 3800fps out of a 22-250 will cleanly take an awful lot of critters. Been there, done that. Have never recovered a bullet in over 50 animals. I would not hesitate to use it on elk in open country.
I will repeat myself, we are talking about kids, A huge amount of variables exist. But letting them pick a rifle that fits, and giving them the range time to become competent and confident goes a very long way to success in the field. Every kid is not the same in mental, and physical capabilities.
We like to nitpick about many things on here, but a lot can be solved simply by shooting a bunch at expected hunting ranges.
