So my question is a simple one- for a young player learning the game and without a deep understanding of batting (either in general or specifically about their own game) what should I be looking for in a bat generally or specifically when we have the infinite options of a custom bat?
Great question! It doesn't just apply to young cricketers but also to older/clubbies who can't seem to find a good bat.
After going thru dozens of bats, retail and custom, the only reason for getting a custom bat made is to
replicate a bat that has served you well.
The custom bats I had had made were based on what I thought would serve me well but in reality were often off the mark. Only after trying many retail/popular shapes, I stumbled upon something that worked well for me. I had that shape replicated by the original designer of the "retail" bat. It worked out great.
In terms of technical specs, nobody really knows or understands what exact measures/specs work for them. It is a crap shoot. Thru trial-and-error, people figure out what weight, shape, length, handle thickness etc. works for them.
If your son already likes a bat and it works well for him, just have the custom bat maker replicate the same bat proportional to your growing son.
To answer your question specifically: you ask for what you know thru trial-and-error. There is no science yet to indicate what works for every individual in a custom bat. Trial-and-error is the key; once you figure out what is working, stick to that shape/style of bat. Let a cricketer's physiology identify what works for that body.