Chris,
First off...it's great of you to take such an interest in your son's blossoming interest (s). I would not have expected anything less from you.
If a revolver, the K22 is a fine revolver to either learn on or as a primary, lifetime plinker. It is also a very desirable .22 and if in good to great shape, it will not be inexpensive. They are very accurate, smooth and are considered pretty top-shelf as far as .22 revolvers go. A wonderful choice, albeit, it's condition (as with most things), truly and quickly effects it's purchase price.
As for semi-auto's.........as has been suggested several times here, the Ruger Mark II is a dandy .22 semi-auto. Smooth, reliable and reasonably priced as there are a ton of them out there. Mine is a bull barrel (target model Mark II), but that is not necessary for most. However, if a used one can be found in such a configuration at a reasonable price.......better yet.
If you happen to find a Mark I for sale (and it wil no doubt be used), please consider the fact that when it's magazine is spent, the slide does not lock to the rear (so as to give the shooter a visual of the chamber and top of the magazine) as with the Mark II's and III's or like most every other semi-auto these days. Safety and general gunhandling teachings are always what we strive for when teaching others, but anything that I can do to further one's safety is also applied when I consider purchasing a firearm. I owned a Mark I and had much firearm training from both the USMC and from being a LEO, but the fact that the slide didn't lock to the rear when the firearm was empty as every other handgun I'd ever shot had done, was unsettling, at best. When my son was of age to enjoy the shooting sports as yours is, I traded the Mark I over for a Mark II. In all other respects, the Mark I is also a wonderfully functional and accurate pistol.
IMHO.....there is no replacement for being safe and ultra vigilant when handling firearms. There are however, ways that we can enhance it. Even though we all know better than to check to see if the gun is empty by pulling the trigger, it is still more often done than what we might believe or want to believe. It seems that it is one of the most universal firearm handling no-no's that happens more often than most all other gun handling mistakes. So.....it helps to reduce the chances of something going bad, even though we've instilled all the safety lessons to those that need such trainings. It also helps to protect our own when someone else might be allowed to use our son's or daughter's Mark I and they are understandably used to all other semi-auto slides locking to the rear and then they handle the Mark I inappropriately based on their previous experiences with semi-autos. Owning a Mark I isn't a recipe for disaster, but it definitely lends itself towards one more so than with the Mark II or III, if only for that reason......IMHO.
If you decide on a Mark II you will likely quickly find that it is more difficult than many to break down and clean. When we find ourselves dreading any chore, we either don't do it or put it off longer than we normally would. A clean firearm is a safer firearm, some much more so than others. The Ruger Mark II's design is not the easiest to learn for many adults, much less a youngster. Then again, it may be the best time to learn such things, as well. Breaking them down by the manual and seeing the internal workings and diagrams is the best way to learn most things. But, if you or your son find the cleaning process to be much less fun than what it should be and due primarily to the "breaking it down" process, I have your answer. Pull up "Majestic Arms" on the 'puter and consider purchasing the $45 (+/-) "Speed Strip Kit" that they offer. I did so when it was first offered in '06 and I can't tell you how pleased I am with the product. I also got quite proficient at breaking my Mark II down prior to the Speed Strip Kit purchase, but the kit made it so much easier and faster that it ws a no-brainer for me. That my kids would also use and clean it when they got older just totally justified it's purchase for me. I woud have to assume that more people would rather shoot their firearms rather than spend more time breaking them down and cleaning them.
Without going into great detail which can be found in the description of the product on the site, I will tell you that it is the best aftermarket item that I've ever seen or purchased in my 40 years of shooting, handloading and hunting.........bar none! You'll strip your Mark II down in less than a minute and more importantly ('cuz its the hardest part for most), put it back together just as fast. Trust me on this one Chris....I've always wanted to do you a couple favors back.
The Mark II is a favorite of mine and my kids and probably will be to their kids as well. It is a very well made, reliable and accurate semi-auto pistol. However, if I were to purchase one, I would without hesitation, also purchase the aforementioned kit for it's convenience alone.
Just my thoughts.
Best of luck and it's great what you're doing for your son.
Ken