I would personally prefer the 7 STW. To me this is a great all around rifle that will shoot flatter and have plenty of energy for anything short of big brown bears. It is true that the 300 will handle heavier bullets than any 7mm will which can be seen as an advantage for an all around rifle, with the high velocity of the STW and todays tough premium bullets i wouldnt consider this too much. Plus, in equal weight guns the 7mm actually will have less recoil energy than the 300 with comperable weight bullets.
Its easy to talk a big game and act like it didnt sting alittle bit after shooting a few shots off hand with just about any rifle, but I would actually have the kid sit down and shoot a .223 or 22-250 of known accuracy from a solid bench rest, and then a big magnum like youre talking about off a solid bench rest, and see how the recoil truely affects his shooting. I would always be really hesitant to start a kid off on a big hard kicking magnum because they will almost always develop a flich that will be very hard to get rid of later, I did.
Also, if hes stuck on the 300 WM, have him take a look also at the 300 WSM
. This is a really cool little round that will balistically match the 300 WM(ok the WM might have a slight edge with heavier bullets but thats just a technicality), and factory rifles chambered for any WSM cartridge have shown an accuracy edge over most other factory chamberings due to their short efficient powder column and the lack of any freebore in WSM chambers. It will also kick slightly less than the WM because it uses less propellant to acheive the same velocity. It can also be had in a bunch of cool litte short action rifles, or in just about any configuration he might want.
Hope this helps.