My son got his first 20ga youth mdl at 10 but did not shoot it much.Then we went out with a 22lr much better choice for a kid to start with in my opinion.
My oldest will be 4 this May. I'm planning on buying a youth bolt .22 (most likely a Marlin) before his birthday. It won't be for him specifically but for my little ones to share and for me to keep. I'll probably buy him one as a birthday present for his 7th birthday. That's when I got my first (a Ruger Single Six). I figure having just one youth-sized rifle for them to share will be best, then getting them 10/22s (or similar) when they're seven will be best, because who wants to shoot a cricket when they're 17?
I don't have any kids since I'm a poor college student. But I received my first gun on my fifth birthday. I got a little single shot marlin if I recall correctly.
I received my first at 6. It was handed down from my Grandfather to my father and then to me. I passed it along to my son when he was 8. I still think it was the most accurate .22 I have ever shot. But then it could have been my young eyes. Some of my favorite memories are of me trying to keep up with my grandfather up and down the mountain stalking squirrels. Grandma sure could fix good squirrel gravy and buscuits.