OP says he's looking for a bolt gun, and asked if 300BLK would be a good choice for it. As much as I like my 300BLK AR, I think he could pick a better caliber for his stated purpose.
Since you reload, OP, you can control recoil with powder loads to a great extent, for the sake of your son. My suggestion for a good paper punching bolt action target rifle that has great accuracy potential, would be a .243 or a 7mm-08. Both are "children" of the .308, both are readily available (brass, bullets, and factory loaded), and both can be downloaded to satisfy the lighter recoil/shorter range you plan to shoot with your son. They are also outstanding calibers for the game you're after, and can be powered up for hunting, and for when your son is older.