I let my son pull the trigger on my Ruger MkII .22 pistol when he was 4 (after getting a recommendation from his Pediatrician about hearing protection...enough of a cotton ball to go into his ear covered with a layer of Vaseline) had him in the back yard shooting a BB gun at 5 (using the prone, kneeling, sitting and standing positions). Got him his first .22/.410 combo gun @ 7, moved him up to a 20 gauge pump and .22 @ 12 (originally got him a semi-auto .22 but have since traded it for a Savage bolt action that he wanted originally).
By age 12 he had shot my 1911 .45, Glock 22 & 23, my wife's Taurus PT111 9mm, bolt action .243 and M-4 carbine. He loves shooting my 10/22 and MKII pistol, but tends to shoot too fast, so I make him put no more than 5 rounds in a magazine (so he's able to change magazines in his sleep now
Oh, I almost forgot, We shoot Airsoft pistols at designated targets in the backyard too, but regardless of what he's shooting or where the same rules apply for all.