I am an advocate of using single shot .22's to teach someone to shoot - much safer than magazine guns, especially semi-automatics. I (and my kids) started with an old Stevens tip-up and a Winchester Model 67. I'm not familiar with what's available new these days.
An alternative for teaching would be single loading a bolt or lever magazine rifle. The previously suggested Marlin 39-A and the Winchester 9422 are good lever choices. I like Winchester Models 69, 75, and 52 for bolt guns, but these are a bit pricey these days.
For semi-automatics, the Ruger 10-22 is available new in many configurations. Remington model 66's can still be found, as well as several excellent old Stevens semi's.
.22's are a great way to learn to shoot, and they make lots of sense for an experienced adult shooter as well, considering the price of center-fire ammunition these days. Keep an eye out for older guns - they are usually priced well, and the corrosion-protective nature of modern .22 ammo usually means the the bore and action are in good shape.
Buck