I started all my kids (at age eight) with single shot youth models, and think that it is the way to go- they'll shoot more carefully/deliberately. 3-5 kids can still burn through a brick of .22lr with amazing speed, even with single shots.
As to which one, I followed Kathy Jackson's (of Cornered Cat) advice and had each kid pick out their own, because if they make the choice, then they are a bit more emotionally invested in the gun, and will see it as theirs. I also made them pay for it with their birthday/Christmas cash. It was fun to go to the gun stores and watch them compare guns, and prices ..... you'd think they were never going to have that much money ever again for all the care they took spending it!
FWIW, two picked Marlin 15Y's, one a Savage Cub, one a 15YS (stainless 15Y with fiber optic sights) and the youngest one spent her money on something else, figuring she'll just borrow her sisters' guns.