I found A definitive guide to sizing a child's bike and Children: Choosing A Bike / Buying a Bike using a search for "size child's bike".
Bike fit for young kids, especially kids who are about to learn to ride, is quite different than for older kids and adults. Rather than being about comfort while riding, it's more about lack of pain when falling off.
The two things I think matter are stand-over height which also matters for adults, and how high your child can lift their feet without falling over.
Stand-over height is basically how high their crotch is when they're standing up. Normally for adults we'd say "a little daylight between crotch and top tube of bike", but for kids I feel at least 5cm is needed, and ideally they'll be able to lift themselves off the bike seat with both feet on the ground. This is about feeling safe on a new toy rather than having an efficient riding position for longer distances.
Foot-lifting height is because kids rarely start by doing the "swing leg over back of seat" mount that adult men do, they lift their foot over the top tube of the bike. Or they try to, and fall over if it's too high.
Other major considerations are budget and community, because they determine how long you're likely to keep the bike before swapping to a bigger one. If this is your one bike until your child is riding to school then training wheels will probably be better than a balance bike. A 5 year old can ride a bike that used to have training wheels, where a big kid on a little balance bike won't work. But if you're in a position to buy a balance bike and a bigger bike, the balance bike will work better. Likewise, if you can pass a balance bike around friends or family and get a second hand bike the same way, it's much cheaper and easier to do that than buy anything.
This was superseded in many ways by a later question about balance bikes but it's worth answering anyway.