If he is on your trust, then he can be in possession, as long as your laws allow a person under 21 to have one. I don't think he can buy one on his own until 21 though, or at least not via a dealer. The laws are dumb, the NFA is dumb, etc.
I have not needed to blood trail any of the deer I have shot with a .350 and the bear creak. All have been one shot, dead within a couple seconds, fall within sight, except a button buck I hit way back. He limped off maybe 40 yards, and I put a finishing shot in him and a dropped there.
I have had a gen 1 and gen 2 ruger .350 with 16" barrel. Now a 16" tikka. All three shot better then I can, but I do like the Tikka more, though it was double the price. 140gn beer creek has done really well for me, think I am at like 8 deer so far, and it works well.
.350 will be easier to...
Lone peak is 375+lbs. My moonlander was under 250lbs, with a maxair fan and insulation. Tent material is harder to insulate, and prone to condensation, plus not great to stay in during "weather". No stealth aspect with the popups, where I can be discrete.
Again, different options and...
A lot depends on what you are looking for as far as features and use case. I like mine so far, and the price is reasonable based on what I, personally, was looking for. Lots of other options out there if it isn't for you.
If you want a durable, lighter, no frills option, check out Radica. They have a bigger model now that might work. I got one of the moonlanders a couple weeks ago, so haven't had a chance to really test it, but the build quality seems really good. Plus, only 250lbs...
Bolt .22 with a silencer and subsonics. Buy a threaded ruger mark iv as well and shoot it with the can and subs. So. Much. Fun. And totally not intimidating.
I sorta think if the only time a kid is in the woods, is sitting still, being cold and miserable hunting, then the odds are low they will stick with it. If you want your kids to turn into hunters, I think having a whole family outdoors lifestyle is probably a way to increase the odds. Camping...