I would go with A1200, as you can see, I have all of them.
The A1200 has all the features that you need and A500 does not have.
I'm not sure what monitor/TV setup you'll use, but for A500 you will need some RGB-composite or RGB-to-VGA converter. On A1200 composite video is standard.
A1200 has a PCMCIA port, which gives you LAN or CF Card, hard to do with A500. CF card is good for transferring files between PC and Amiga.
A1200 has a HD, A500 not. For your child to enjoy Amiga games you NEED HD and WHDLoad, trust me, kids today are not too patient like we are and will not wait long to load games and don't get me started on multi-disk games and the swapping it can cause.
As far as choosing A1200, I would go with Amiga Technologies version, that what I have. I think they are more reliable. It's been running weekly w/o problems and it's still sitting on my desk getting use.
Or other Alternative, CD32.