I own and reload a 7X57...
but have no experience with 7RM.
My 7X57 reloads chrono at 2,950 fps MV for a 140 gr bullet, with 1.25 MOA accuracy.
At that velocity, I do get a little recoil, but not enough to bother me.
If your teenager is 6' 6", and 200 pounds, the 7RM recoil might not bother him much, so I think you should let him practice with that, while you practice with the 7X57.
Each rifle is an individual, when it comes to trigger pull, so you should practice with the one you will hunt with. You definitely don't want to "click it like a ball point pen".
Practice by "dry firing", i.e., squeezing the trigger on an empty chamber. To prevent possible damage to the firing pen, buy a "snap cap" and put it in the otherwise empty chamber for practice. You will probably have to buy a 7X57 (and 7 RM) snap cap from Midway, Brownell, or some other catalog, as local gun shops and "big box" sporting goods stores usually don't stock snap caps.
After about 100 repetitions of dry fire, weekly, you should go to the range at least monthly from now until deer season, to live fire, at least 20 rounds per session.
Artillery lends dignity to what would otherwise be but a vulgar brawl.