After assisting my grandson through AK Hunter safety, on his 10th birthday, I gifted him his first rife.
The kid shoots tight groups already with .22 & 223. Has been on three moose hunts.
Any of those would be good. Honestly a 7mm rem mag really doesn't have much recoil. Neither does the 270 or 243 etc. I would let him pick the gun itself he likes and simply see what cartridges are available in it. These days picking a cartridge that's affordable and you can find is a good thing too.
Also is a good idea to double up, say you have a 270 if he got one too it's less ammo types to buy. Just don't be like my dad and inadvertently stick a 270 round in a 7mm mag, it will chamber and fire, exactly 1 time.