.223 is too small the worst thing that might happen for a kid is to shoot a deer with that.... and lose the deer. That risk is obviously ok for a lot of people on here as they don't appear to be trophy hunting but rather just shooting "deer". I guess if they look for it for 5 minutes and don't find it.... they just shoot another one. If there is no reason for it...then why open up that world of possibilities?. If the kid can't handle the recoil only then does that become a different story IMO.
.350 will smoke a deer. That's what I would get. I always see ammo available which is a separate issue but something to consider moving away from .223