Okay, you're picking up a rifle for the 17-year old. To mis-quote a comedian, "how big a boy is he?" At 17, I weighed in at 155 pounds on a 6-foot frame...pretty lightweight.
You won't go wrong at the end of the day with either .270, .308, or .30/.06; the shells for each are fairly available. The .06 is maybe the most versatile in the number of different loads available, from varmint to grizzly, but the recoil can affect anyone.
My wife shot my old .06 for a couple of years, but last summer wanted her own gun. She settled on a Tikka (made by Sako) in .308. She would have gotten another .30/.06, but the Tikka was lighter than my old Springfield, so she figured the recoil would be about the same. The Tikka actually kicks her a little harder, but on the stand, she doesn't notice at all.
Remember that some of the recoil can be tamed by a PAST or other shooting pad in addition to the recoil pad on the gun. Laura found that shooting from the bench in warm weather required a pad, and that from the stand in November, the thick clothing just about made the length of pull equal. Again, when she puts the scope on a deer, she never notices the recoil...
My personal experience has been with the .06 and the .308, and I'll recommend them any day of the week. Both are capable, lethal rounds well beyond the distances you have stated, and shells can be had about as easily as you'd want.
Another idea...do you know anyone with a .270, .308 or .30/.06 you could borrow to test out?