An ACCURATE bolt action with iron sights would be my recommendation. That is a gun that can grow with the new shooter.
Regarding an auto-loader, one other consideration is that their operation is more complicated than a bolt action's. A few years ago a buddy of mine asked me for a recommendation for a .22, and I said, on a limited budget, a Savage bolt action would be my recommendation. Well, he ended up buying a Savage autoloader instead of a bolt action, I think because he thought it would be more fun to have a semi-auto, but he has had a lot of trouble with it because he has had trouble getting it adjusted properly (a bolt action would have been more fun considering the problems he's had). I know the 10/22 doesn't have that type of problem, but I would still recommend a .22 bolt action for a new shooter.
If money is no object, there are a number of good accurate bolt action .22s. Anschutz, Cooper, and Kimber get good reviews, and .22s are available from NULA too, but for a new shooter I would lean toward a CZ 452/453/455 as a great "mid-priced" .22 option or a Savage as a "budget" option.
Important - be sure to get one that has a stock that is the right length for the new shooter (or be able to make adjustments). If stock fit is an issue, a AR-style rifle with adjustable stock in .22 LR configuration would be a good option if it was used as a single shot by the new shooter.
