I guess we have options now. When I was younger, we just took the old rem 700 out with a mixed bunch or differing weights if rem soft points and made the best of it. Those old steel butt plates hit the shoulder hard, and heck, we got bruises on the shoulder and face from the old JC Higgins pump 12 gauge that we'd take goose hunting. We thought nothing of it and actually enjoyed it! With that said, I have a teen daughter that lives to hunt with me. I had tone down my redneck tendencies and make it enjoyable for her.
I bought a7mm-08 Tikka Compact for my daughter when she started hunting at 10. She was so small at that age. We loaded it light with some 139 SST's, but we found it was better for her to shoot my varmint 243 with a heavy barrel because the recoil was not pleasant with the tikka compact. The short barrel produced a lot of blast and it honestly smacked the shoulder pretty hard. We made her hunting trips all about her - I just pack the heavier rifle and the meat!
She ended up taking 4 elk over the past 6 years using a normal sized tikka t3x in 7mm Rem Mag. I load it with a lightish charge of reloder 23 behind 162 eld-x's traveling about 2880. They shoot crazy-small bugholes. With a 4 port TI Pro brake on it, the recoil and "snap" is significantly less than the '08 compact without a brake. When it's loaded near max the recoil is significantly more.
At 18, she's finally able to pack the 10lb rifle/scope setup on her own. Almost all shots with the 7mm RM are taken prone or seated/kneeling with a harris bipod - that's just kind of how I taught her. We hunt primarily mixed/open country with lots of shots across canyons or draws, so this suits us well.
From my experience and preference, depending on your hunting style and terrain, I would recommend a brake/can for a young shooter unless you go 6mm or smaller. Just don't forget the hearing protection for the brake!