I agree with most of whats said above, and especially that you should be the judge of whether or not your child is responsible enough to handle a pistol or not. Obviously if it is against the law, and he is aware of that, he will be breaking the law if he takes one of "your" handguns out of the house without you or your permission or if he takes the handgun "you bought" that was for him, so whats the difference. You know he is either responisble enough or not, and you shouldn't let anyone make that decision for you.
I also agree that a good Ruger single six in 22lr would be a great first pistol, easy and cheap to practice with, and we all know that shooting a pistol is a very different act than shooting a rifle and usually takes most people considerably more practice to be efficient, so cheap ammo and low recoil is a very good thing. I was packing a Ruger Blackhawk 357mag at age 14 back home when I was in the woods, shot lots of grouse with it using the bird shot, don't know if it was legal or not, took it to school and made a set of grips for it when I was 15, with knowledge and permission of the school prinicple. No one ever said anything, but that was back when the parents decided whether or not you were responsible enough, and it certainly wasn't in this state. Personally I think a revolver in 22lr would be an excellent present for a 16 year old. I used to have a double action medium frame 22lr made by Dan Wesson, that I would almost give a left nut to have back. Check the pawn shops and gun shows for deals like that.