I strongly recommend the Freeport Junior Club to anyone wishing to have their under-21yo children learn how to use firearms. The guys in that club are patient with kids, talk to them in a fun way and willing to spend time with them. For $75, it's a bargain! And, after the 14+yo's take the online portion of the NRA Basic Pistol course, the Range has NRA Instructors that will qualify them for Part II of Basic Pistol (live fire), as part of their membership. If you enjoy target shooting, it's a great way to participate in an activity with your kids.
For handguns, they start them out with .22 cal revolvers and over time, .22 cal semi-autos. With more instruction and training, they'll eventually be able to use centerfire revolvers and then semi-autos.