When my eldest daughter was approaching her 5th birthday I bought an Apollo 16" BMX from the shop a mate worked at. It was perfect, 14mm axles, A-head set and Dia-Comp brakes with adjustable spring tension. I think was about $320. The paint was a lame, powdery, fluro orange but since it was to be a 'girls' bike I stripped it and painted it pink, laid on some flame graphics and clear coated it. I don't think she would have minded the original colour, but I wanted it to be special.
She is now nearly 8 and ready for a bigger bike. Unfortunately darling wife and I are both studying and money is tight.
My second daughter is learning to ride, but is not enamoured of it like her older sister or her younger brother...
My now 4 year old son started out at 2 1/2 on a Stride-to-ride bike and then graduated to a S/H 12.5" BMX. I didn't put training wheels on it, because I think they stop you learning how to steer. He wasn't really getting it, the rear tyre always went down even though I put in new tubes and checked the tyre for thorns etc. The bike sat through winter in my shed and then I took the eldest to the MTB Park on the school holidays and the campaign began...
"Dad, when are you going to take me to the MTB Park?" he would ask. "When you learn how to ride," I would reply. After he pointed out he couldn't learn to ride without a bike, I got in and fixed it. In a day and a half, he went from being unable to ride to being able to start off by himself. He was just so ready to do it.
After a week it was obvious the 12.5" was too small so I pulled out an old 16" that a mate had given us and repacked all the bearings. I put a riser bar on for him rather than the BMX bars and he's stoked.
Yesterday we rode to kinder and back and today we will ride again. The bike is a bit of a POS, but it rolls well and fits OK. I cut the bars down, but they are still pretty wide. The back pedal brakes are a problem for more ambitious stuff (the MTB Park was sketchy as) so I've negotiated to buy the bikes my shop mate had set up for his son.
I'll say this, if your kids are ready; get them onto any bike that fits them. Don't muck around saving for "The Bike" get them riding while they are in the sensitive period. Then save and get the good bike. They won't care about having a flash bike, they'll be happy to be riding with you.