Here is my opinion:
If playing games is the overall goal, go for the a500.
If you want something (maybe just a little bit) more than just being able to play games, then go for the a1200.
You can connect a standard IDE harddisk to the a1200, but you´ll need a cable, as the a1200 has a 2.5" connector on the motherboard.
As a plus, an a1200 with a HD, could get games installed on the HD, which in many cases is nice. Also many old disk-only games have patches now,so that you can install them to HD. You would then need some extra memory though..
Anyway, you shouldn´t go out buying a brand new amiga. Get one used, try
amibench