I would wait until he was old enough to know that he likes to shoot before I went out and bought him a gun. He may grow up and not enjoy the sport.
If he decides he wants to shoot, let him pick the one he wants with your guidence. That way he is happy with "his" gun and not overpowered too soon since you helped him.
The biggest mistake my dad ever made was making my shooting decisions for me. I loved to hunt and shoot, so I put up with his choices, but still didn't go sometimes because I didn't like have a gun that was wrong for me (still don't like turkey hunting for this reason).
My brother liked to hunt, but when given what he was going to shoot and not asked, he went the other way and hasn't been in the field in over a decade. Just something to consider.