The Browning X bolt compact that my oldest daughter is currently shooting is a joy to shoot with the HSM low recoil rounds. They are 140 grain bullets and the gun really likes them.
That being said, I’m not sure I wouldn’t get a 357 single shot that shoots 38 special. Can practice cheap, sight it in for 357 rounds, let them shoot 38’s practicing and 357 hunting. Keep shots within 100 yards….which most people ought to be doing anyway.
The AR idea is a good one as well.