I bought my son a Rem 700 7mm-08 when he was 6yrs old. He is now 10 and has 8 Texas whitetails and several hogs to his name.
I have been loading it with reduced 120 grain ballistic tip loads and will slowly work him up to full strength loads as he grows.
I had the original tupperware SPS stock cut down to 12.5" when he first started shooting but have since dropped it into a B&C stock that is 13" LOP and he shoots it just fine.
If your not a handloader Remington makes a reduced recoil load that is really easy to shoot.
Good Luck!