when i introduced my sons to shooting it was with 22 rimfire single shot daisy bolt action rifle. it was a good tool for training but they got bored quickly with the single shot.
if i were to do it again i would look for a "youth" sized 22 bolt action repeater, something with a detachable magazine. this would be as safe as a single shot but would allow them multi shot capability as they gained experience.
single shots of any type are nice, bolt actions are my recomendation, lever and pump rifles are almost as good but i like the removable magazine guns better. i would not recommend a semi auto for any beginer. even if the child handles a semi auto safely i have found they just like to pull the trigger and hear the noise and see the dust from the bullets. it is too much fun for a kid to hear the bangs and see the dust where the bullets strike to teach them good marksmanship.