I personally like the Leupold and Burris Compacts.

If a scope is a must (I think everyone should learn and be able to use iron sights) and it's to be just a youth plinker, go with a Simmons or - gulp Bushnell. I use Simmons on my plinkers and am pretty impressed with them for the cost. If I need better, I use Burris.
Still would get him used to irons. Optics fail but irons are always thereas a back-up if needed.

you could always buy a red dot.

Cheap or expensive, don't put anything on your son's 10/22 unless it has a one-inch tube!

Personally I like Leupold scopes, and Leupy makes three scopes that would work great on that Ruger .22LR. A 4X fixed, a 2-7X variable and a 3-9X variable with adjustable objective.

For a cheap 1-inch scope, a Bushnell 4X or 3-9X promo scope didn't use-to-be a "bad buy" for putting on a .22LR.

Give consideration to putting a shotgun scope on it. Most of them have long eye relief and are non eye relief critical. If your son is of normal stature for his age, he won't have to crane uncomfortably in on the scope. He'll be able to assume a very natural position. I have a fixed power Tasco shotgun scope on mine and love it. You don't have to spend a fortune...despite what many here will tell you, to get a fine scope for your intended use.

Get a Simmons 4x ".22 mag". Dirt cheap and work really well. I had one on a Ruger 77/22 .22 magnum. It was a silly/stupid thing that worked way beyond my expectations.

Tom