The 30-06 has a good bit a kick to it but it is quiet managable. This can be mitigated a bit with a good recoil pad added to the gun or better yet a heavier than your standard weight gun such as one with a laminate wood stock and bull barrel can render it pretty mild recoil wise. Of course shooting heavier bullets in it at full throttle loads will put a little more ump into the recoil on it too as compared to standard 150 gr loads.
If this is your first centerfire rifle I would suggest that you start with something like a H&R Handirifle in 30-30 or 223 which is a pretty budget priced gun, with low recoiling rounds that will help you master shooting well before you step up to something that has more recoil. Developing a flinch from starting out with a heavier recoiling rifle is an easy thing for a new shooter to do and a very hard habit to break yourself from once you have it.
Now that more info has been posted...
I think a 30-06 is a bit much for a 15 yo. A Handi Rifle in 30-30 or 243 would be a lot more sensible gun to start them out with. I think they may also make this in a 7.62x39 and if so this would be a great caliber to start with. However understand that most American Manufactures of guns in this caliber sport a 308 in bore not a 311-312 bore and you will likely want to use american ammo instead of surplus or foriegn made ammo.
Yes, as long as he sees the father handle it well he will emulate what he is shown. Proper placement and follow through being key to teaching good habits. It will kick a smaller bodied person pretty good but I suspect he will not say a word.
My shooting sessions with the 8mm and the 30.06 run under 75-125 rds each and during that time I'm bound to slip up and get a sore cheekbone or shoulder about every dozen or so times out. The large rounds are an experience game. give him 10-20 rounds and tell him to save what he doesn't want to shoot right then.
The bet is all 20 will be gone before you look up from your own rifle. Reminds me I still need to get my .06 proofed and give the 03 back.