300 Win Mag or go home.

I kid. I was shooting a .243 at that age and had no issues what so ever with it. It was my granddad's rifle and now it is mine. It will be what I give my son when he gets old enough. Never shot the 7mm-08 so I have no opinion one way or the other. If neither of those appeal to you then there is always a 25.06 or a .223.