Steel Challenge is a great place to start young people shooting because there is not a lot of movement and other complicated courses of fire to shoot. Rimfire handguns and rifles are fine for this type of competition. Atlanta Conservation Club hosts steel matches as does the RCC in Terre Haute.
Kids under adult supervision are allowed and encouraged in USPSA comeptition as long as they can be safe while shooting the courses of fire.
What type of shooting sports? Rifle, Pistol, Shotgun? If looking for shotgun (Trap) I have some leads. My son shot in a youth program for several years.
There is a nationwise scholastic skeept, trap, and sporting clays organization that has been growing for several years. The is now also a USPSA/SCSA-affiliate scholastic steel shooting program as well.