Ok , I own 2 -.243's , 1 - 7mm-08 , 1 - .270 , and 1 - 30.06. , amongst othercalibers.

If it is just by your criteria , and I look at the performance of those guns, I would have to say that the 7mm - 08 is ideal, and the .308 is close but for the recoil limit. My 7mm-08 is a rem. model 7 ( short and light ) , the .308 is a Ruger M77 stainless / syn. ( full size and heavier ) but it is a tack driver too.

But I want to throw one more kink in the mix.

A 30.06 or a .308 using Remington Managed recoil ammo. It has the recoil of a .243 or a little less, and is good to about 225 yards on the normally thought of idea of needed energy for medium sized game. I got some for my wife and her 30.06 and they shoot great and work well. Then if you want, you can shoot full strength loads whenever you want, or if you give it to your son, he can shoot what ever he wants to shoot. It really is a very viable option for you, and I think you would like the versatility.

I would at least say check it out before you decide, then if not look real hard at the 7mm-08. That round has dropped a lot of deer for me over the last 16 years. I was shooting that round before it became the popular stud it is today.

Good luck and God Bless.