My son was still 14 when he shot this doe with a 7RM Sendero:
First Long Range Kill
The weight of a Sendero and the brake make a huge difference.
He had already been shooting about 4 years working up from 22LR, 223, 25-06, to 308.
In any case, you want to keep it fun. e.g. 22LR with reactive targets such as balloons or water jugs
243 Win or 260 Rem would be great choices.
Get a 7RM or 300 WM for yourself and let him borrow it when he works his way up to 500yd Elk.