They grow out of them so fast - it is not worth buying new. At least in the early stages. However for Smallsteps, the bike has to be light enough as she is pretty slight. If it is too heavy, she struggles a lot. The bikes that are cheaper weigh about twice as much - and last about half as long. Her current bike is new because the only ones we had available to get used at the time were the heavy ones.
My wife and I still use my parents old bikes.
I have my father inlaw's bike - but don't ride it. Most of my injuries have come on two wheels :D