I started with a Remington 514 .22 BA single shot at age 7; couldn't hit a thing with it when hunting--OK on tin cans. Spent "prune season" picking prunes at .25 a crate and when I had my school clothes paid for, I still had the $23.50 needed to get a Winchester "Steelbilt" .410 SS with a 28" full choke barrel. Basically, I used it to pot shoot ground squirrels and jack rabbits until I was old enough for my granddad to give me a Win. 92 .25-20, and I got a Win Lo-Wall .22 WRF for cleaning out the neighbors' sheep barn. Didn't use a shotgun again until I got a Stevens 5100 double 12 with 30" barrels in junior high. You HAD to swing that thing! I also had a Peiper hammer 12 that was just as long and heavy, and those are what I used to learn to wingshoot. Killed pheasants and quail with them fairly well by the time I was in college. But I took the .410 to school with me and used it for hunting quail and chachalacas in Mexico and Southern California, and still have it. Mainly use it for cottontails now, along with a Savage 24 .410/.22WRM.
I wouldn't start a kid with a .410 now; a 20 has much more flexibility and cheaper shells. I agree with ClapperZapper that a .410 tends to promote aiming in the untutored young. But I have always loved .410s and plan to get another as soon as funds and fortune (meaning finding a decent one at a decent price--LOL) allow. Killed my first little blacktail buck with a .410 slug from that M37. You need to get very close....but slugs are very practical in my Savage combo gun (I sit a scope on it and handload the "LightGame" slug).