@sharpie
Ok I think you are being provided with perhaps too much information at the moment :-)
For a nice system that will play most (not all, though) games, you'd like an A1200 with an internal hard drive (needn't be big, a few hundred megabytes will do it) and perhaps some extra memory. Extra memory can be had as such, or together with an accelerator. An accelerator may speed up a few games a little (most games were designed to work with an A500 anyway, so an A1200 is quite fast enough), but is not really necessary.
An A500 with a hard drive is of course a possibility too, but then you will miss out on those AGA games, there were some good ones too!
You can probably find a nice A1200 setup at EBay for a good price, I suggest you go do some hunting :-)