For a 13 year old it depends on your size and your experience with dirt bikes, but an 85 is usually the best size bike and fastest for a 13 year old. Unless you are really tall which you would need a 125.
4 years old you can race motox. (50cc class)
Kawasaki Kx500, any year will do, but the best bike for a beginner is a Yamaha yz490
The best bike to buy for a nine year old active boy is a 24in-wheel bike with a 3-speed hub gear.
Yamaha also know your hight and weight.....i race em and am only 16 so if ur buying, then know those things.
It depends on your height and how you can control the bike. My first bike when i was eleven was a Honda CRF 150F.
Probably a yamaha ttr 110
A 125 two stroke or 250 four stroke would be good power wise. Just make sure the bike fits for their physical size.
an exercise bike would be the best start
250 cc is the highest a 14 year old can have on a street bike
The bike that you should think of buying an active 9 year old is a 24-inch wheel bike.
A 13 YEAR OLD CAN RIDE A MINI BIKE AS LONG AS IT IS NOT ON A PUBLIC STREET.