I see a lot of good suggestions on this thread. Having worked or lead youth hunts for several years now, I've had the chance to observe the shooting capabilities of hundreds of beginners. Some of my observations:
- Those who come with an AR platform (especially with adjustable stock) typically don't go home with empty coolers if the animals cooperate. 300 BLK and 6.8 SPC have both proven themselves. From my observations, I have to conclude the ergonomics and recoil management of this platform is just superior to everything else out there.
- Suppressors boost confidence (a big factor in shooting ability). Suppressor combined with AR, even better.
- Gun fit is paramount. It helps manage recoil and the ability to see through the scope easily. I made the mistake of buying my son the H&R rifle for his first one and neither of us could shoot it well because it wasn't comfortable to shoot. It might be for some kids, but not for either of us, and he wasn't that big at the time. I was 6'3", 225#, and I didn't like shooting it at all. Turned out the geometry was all wrong and amplified the perceived recoil. Limbsaver pad helped some here, but it still felt wrong for both of us. In spite of that, he took his first deer on his first hunt with perfect shot placement.
Regarding that last one, I recently had a dad call me night before the hunt: "..we got a problem..". He explained that his daughter was having a problem shooting the gun, possibly due to recoil. I had him bring the gun; I brought all 3 sizes of Limbsaver slip-ons plus my .257 Roberts just in case. At the bench, we fitted the pad first. After that, I could see she was clearly uncomfortable with something. She said she had a hard time seeing through the scope. I noticed it was turned to 9X, turned it down to 6X and had her try again: "That's great!" She proceeded to shoot the best target of the group. She was the first to fill a tag and also tagged one at 200 yards. I believe she had a .243 bolt gun. Yes, .243 can be intimidating to some; everyone is different in their perception of recoil. I've spent a lot of hours trailing bad .243 hits, but well-placed shots do the job every time in all of the calibers.
Above all, be patient with the kid. The hardest thing I've had to do is watch parents (both moms and dads) get impatient with the kid because they're still learning or they can't tolerate what they perceive as minimal recoil. Some parents are good at it, others aren't. Patience and observation on your part is a key factor in their learning experience. Make sure they're having fun.