I received my first gun - a .22 bolt action rifle - when I was 11 years old, then my first shotgun - a .410 pump action- when I was 13. When my son is around 11 or 12, a .22 rifle will also be his first gun.
I don't think a handgun as a child's first firearm is good idea. I didn't receive my first pistol - a .22 rimfire semi-auto - until I was 14.