I went a different route with my two sons when it was time, but I'm not sure now if it was the best route. It wasn't a bad route either.
I couldn't see giving them a single shot or bolt action that shot 22lr. To me the 22lr round was intended to be used in a semi-automatic firearm. Once they had graduated to a semi, they'd not hold much interest or use for a single shot or bolt action in 22lr, that was my line of thought at the time anyway.
I wanted to give them something that they would keep and could find useful throughout their lives. So each son received a magazine fed bolt action 22wmr rifle on their 10th birthday as their first firearm of their own, which initially were treated as single shot rifles.
I own several myself and still enjoy them a great deal despite how pricey they've become to feed. I'd bet I spent as much as I did on the rifles just feeding them ammunition as they learned and enjoyed shooting them, maybe more. I know that I have since.
Each had to meet a certain level of consistent ability with iron sights before they were allowed to graduate to using an optic. They each did receive a 22lr semi-auto of their own as a later gift, but neither before they were 13 years old.
I'll admit that they had already been exposed to ones that I own before they received one of their own.
Some years back I had an uncle pass away, and I was given a Savage model 63 that had belonged to my grandfather, his father. It was beyond rough, and I brought it back to life by replacing a few small parts from Numrich as well as the stock itself, which I was surprised to find that they still had available as 'new old stock'. I also added a period correct Savage 4x scope to aid my old eyes (though not the scope that the rifle had been marketed with), and a very cool leather sling with the Savage logo embossed on it.
Earlier this year I found a Ted Williams version of the Savage model 49 lever action that brought back fond memories of myself with a couple of close friends and our adventures together in our early teens and I had to have it. The one we shared in those memories was not mine, but in essence it is now.
Both of these rifles are single shot despite the difference in their actions. Both shoot 22 short, long, and long rifle. Both load and eject empties quickly and easily, and both are virtual tack drivers with the right ammo.
I'm surprised at just how much I enjoy shooting them over all of the other options that I own.
I'm also thinking that when the day comes to introduce my future grand children to shooting, I may do things differently with them than I did with their fathers.