BOLT GUN!
Don't let them learn the concept of "It's Ok, I got another shot" like they would with a semi-auto.
They WILL think this, I have seen it many many many times in a state where a ton of kids are involved in shooting.
Nothing is wrong with the Ruger 10/22, probably the best semi auto 22LR around, with hands down the most available "enhancements" (It is the 1911 or AR of .22LR Rifles)
I would recommend the Ruger 77/22, bolt action, EXTREMELY accurate, uses same magazines as the 10/22. The only issue on this suggestion is the price tag.
Looking at the reliability and "overall cost of ownership", the 77/22 is an Excellent Bet for not failing, and being relatively cheap to repair if something does go wrong. I cannot say the same for Remington bolt .22's.
Pump Action .22s are around, but they are cumbersome and confusing.
Another option: NEF Handi Rifle in .22LR : $250 after you put a cheap optic on it. Break open single shot, amazingly accurate. I would recommend this over some lesser bolt gun if worried about price.
If you are teaching 1 shot, where you want it to be, you want to start on an accurate platform. That would be the 77/22 (match grade out of box), or the Handi Rifle (extremely accurate, and affordable).
Again, I do not recommend starting somebody shooting with a semi-auto, it is akin to giving them a Porsche for their "Learning Car".