Some have suggested the 7-08 for it's flat line traj. and hitting power. I have not had any experience with this cal.
From another thread:
As a hunting Canadian I have used a 7mm mag for everything from moose to deer to elk to bear. You can't match the 7mm mag's fire for effect.
You realize that the 7mm you use is the same caliber as the 7-08 right? You do have experince with that caliber but maybe not the 7-08 as a cartridge. "Cal." (caliber) is not the same as cartridge.
Now then, the 7-08 is a great shooting and more than adequate deer cartridge. My brother actually took a decent sixed moose with one years back. Other cartridges to look at would be .257 Roberts and . 250 Savage The 7-08 ammo is more available though. One idea might be to look at he remington youth models and se what chamberings they come in for a particualr model and go with one of those, When your son grows, simply change the stock for a full sized one and he can continue to use the same barreled action. Model 7 is a good start for this.