If you think he can take more recoil than the 7mm-08, then I would recommend the .308 Win, obviously, judging by my name, I use one, and I love it, I am, however, 14 years, and a somewhat thin guy, so I can move with the recoil a bit, but in case you do decide to go with the 7mm-08 rather than the .308, I would make just one recommendation for anyone who's starting their kid out on rifles, get some shooting bags that are specially made for the purpose of being a rest for shooting off the bench at the rifle range, so that they can shoot their gun, and know that it isn't going to hit them, it isn't going to hurt, and there's no rush, and no trying to aim the crosshairs so much as to put the crosshairs on the bullseye, which they'll stay on, and it all becomes about just pulling the trigger.

The purpose of this isn't really to improve their aim so much as it is to let them trust their gun, and not worry about the gun, so that that fear factor is significantly reduced of the gun causing harm to the shooter, which it doesn't.
In this way, it'll help the kid in having that rifle be an "extention of his arm", because he's going to respect it, but not fear it more than he should, which ultimately, results in greater confidence, and better marksmanship.
There's no such thing as taming a gun, it's the shooter that must be tamed.