Either 6.5x55 Swedish Mauser, 260 Rem or 6.5 Creedmoor will be your best options, with good rifle and ammunition (120-156 gr bullets) choices to be found.
Another great choice is the 7mm-08 Rem (again 120-160gr bullets).
If you want something a little lighter and still very effective with a classic touch, the 250 Savage (also known as the 250-3000, with 87-100 gr bullets)) is another great choice.
These choices will also be great for target shooting, as recoil is fairly mild, especially with the lighter bullets up to 143 gr. But find a rifle that fits him well, or get an extra stock that you are not afraid to shorten and fit with a good recoil pad, and then are able to put the original stock back on when he grows larger and can fit the original stock's length of pull.
Also hard to beat the good old lever actions in 30-30 (150-170 gr bullets) or the 35 Rem or 38-55/375 Win (200 gr bullets) if looking for something with a larger bullet.
Although the latter 3 will be limited to just over 100 yards. But not a bad thing for a young hunter to learn to hunt and gain stalking skills on game.
Everyone should learn to shoot rifles with open sights at various ranges. It is more of an acquired skill that provides a better sense of accomplishment. Many levers can be fit with scopes, but to teach him this skill is important, and he will appreciate the capabilities of the scope more when using one.
May not be the typical target rifles or cartridges, but are a lot of fun to shoot, carry and hunt with!
There's something about using levers with open sights that just cannot be found when using scoped bolt action rifles, and should be experienced by everyone.
Just my 2 cents...