Can I be the odd ball and reccomend the 280 Remington? It can be loaded down to 7-30 Waters level (just like the 7-08) and can be loaded with heavier bullets for the day you take the young fella elk huntin'
On a more serious note, I think the 44 would do ya proud, and I can attest that a 265 grain bullet at a sedate 1300 fps is murderous on deer and gentle to the shoulder and not so loud as to be disrupting to learning. It is a far more decent learner than the 30-30, but rest assured, he wouldn't be the first in the field at 13 with a 30-30.