i got my first car when i was 16 and i put $1500 for the down payment, it wasn't a super nice car, but it was a nissan sentra with super low miles. my mom registered it under her name and then when i finished paying it off within 3 years, she signed it over to me. i think i would do the same for my kids too, i worked really hard to get a car when i was 16. they would have to show the same dedication i did as well.
I was nineteen... It was around last June or so. My father gave me his old car when they bought a new one. I probably would have had a car sooner, but we didn't really have the money to do so, and the one job I did have in High School was so high stress because of the lack of work from the other employees that I ended up having to quit so that I could focus on school instead of coming home tired and pissed off every night.
As for my kids... I'm not sure. It really depends on our funds, and how responsible they are when it comes to who buys it, and when.