have you thought about a 'run bike' ? (bike with no pedals) its a good first bike for teaching balance and gives them speed etc . mine all started with run bike and progressed to pedals really easily without the need for stabilisers. puky do one. but the first one we got was from ebay, sent over from germany i think. there are lots of wooden ones about too, but i worried about how long theyd last if they were left lying around the garden in all weathers.
Mmm. we will be doing this in a while, so no personal experience. but friends who have say that if you get something cheap then the brakes are too tough for little hands, and the cranks are too long for little legs, and basically the whole experience is often so unpleasant and such hard work that child is put off riding. The make folk recommend is Puky - but I think it is EXPENSIVE, maybe you could find a second-hand one?
On sizing, I'd go into a shop and ask them what measurements they'll need.