I'm going to throw out an unconventional suggestion here that I hope will provide some food for thought. First, check out the following link:
http://www.jamescalhoon.com/
Check out the "informative articles" section under the title: "To Bee, or 223, is that the queston?"
If you are a handloader, I would highly recommend acquiring a savage model 11 in 223. It is available as a youth model as well. If you shop carefully, one can be had used for $300-$400 or about the same as it would cost you to buy a mid-quality rimfire.
Using information from the above referenced article as your starting point, you can cast your own bullets and produce very accurate handloads that duplicate rimfire type ballistics. Done this way, brass life is virtually infinite and you can roll your own rimfire class loads for the same money or less than it would cost you to buy regular .22LR ammo. If you are someone who likes to shoot match ammo in your .22's, the cost savings and performance advantages are considerable.
Additionally, as your son's shooting skills grow, you can step up to .22mag class loads, .22 hornet level loads, or normal 223 loads without having to buy another rifle and scope.
IMO, the flexibility and economy of doing this sort of thing make for a pretty compelling idea.