What state is he going to be hunting in? Some states restrict you to shooting only shotgun.

Buying used is no doubt the cheapest way into this. Since the objective is to get him into the game, don't get all wrapped up in buying something expensive. When was the last time someone missed a deer because of using a worn-out firearm? Clean it up, maintain it properly, and it will shoot.

On this theme of getting into the game cheaply . . . a scope is not a necessity. A rifle with open sights will still shoot and kill deer. I think I read somewhere that over half the deer shot in the US are shot at under 100 yards. If you can't shoot a deer with open sights at under 100 yards the fault is with the shooter, not the gun, not the open sights.

Having said that, every big game rifle I use has a Leupold VariX III or a VX-III on it. But I appreciate that this is not necessary to get started.