I know this thread is old, and Tank's already had the kid out hunting by now, but I wanted to chime in on the 7.62x39.
I have one WASR 10 that spits out 154 gr wolf soft points and has reliably killed one 8-pointer and several does the last two years with no follow up shots and devastating wound cavities, shot distances ranging from 30-225 yards. In all instances, smallish hole going in, large gaping travesty on the off side and slot of destroyed tissue.
The 260 rem needs a long barrel. To achieve it's optimum performance, 24 in is ideal. I have a Ruger Mk 11 with short stock and 18 in barrel and it leaves much to be desired in terms of accuracy, but it is light. My mom now uses it.
.308 is a bit heavy for a kid, but if he's up to it, then I'd say go for it!
No experience with the 6.8, other than ballistics research. Think I'd prefer to be caught on the trigger end of the 300 blackout.
I've used (legally in my state) the 5.56 NATO for deer. Before I'm bashed, it is legal in my state, doesn't tear up meat, and is more than adequate for taking big MO whitetails. Speed is the killer with this round, pass throughs are indefinite at 0-300 yds, and it has no recoil. I do not feel under gunned with my lil 223 rem, as it accurately puts Barnes Vor Tx tsx in the boiler room, and no runs past 30-40 yards. There's another option if PA let's you use em.
As for x39.... I've heard folks scoff at the idea that the Russian shorty is the twin of the 30-30. Bull hockey. The trajectory of the x39 is flatter past their "twin" ranges, and the x39 will carry more energy upon arrival. 100-200 fps is a substantial difference when comparing the two, and the 30-30 just plain pooters out quicker. IMHO, I would not be caught choosing a 30-30 over a 7.62x39. The Saiga I'm getting this Friday is going to replace the WASR with it's so-so accuracy, and become my new deep woods gun. I don't expect sub MOA, but it will do it's part.
It's a great country we live in when we can have choices.