I also think a .22 LR is the way to go for a new shooter. He is asking a lot by needing home defense, deer, and small game. Really needs 3 different weapons for those.
Go with him to some pawn shops, ect... and look for a good used one.
Start with the 22 simple rifle, works for small game, and practice.
If he likes that, and proves proficient, then:
Home defense would be a 12 gauge pump, Mossberg 500 for starters.
Then a Savage model 100 for bigger things.
Just my opinion for a new shooter.