Hiya Dew-it. Good luck on your search. For games, the A1200 is the ultimate machine, especially if you can get it with a few gig HD (in order to put all those WHDload games on), an accelerator with some RAM, and a CDdrive. For the CD, you have either the option of a SCSI kit (that goes with Blizzard type accelerators) or a SquirrelSCSI, if you want to stick with SCSI devices. Some people have modified their 1200's to fit a laptop CDdrive inside the machine, since the HD connector in the 1200 is IDE. With a special connector, you can have both a HD and the CD together. You'll need that to play CD32 games (if you find any).
The nice thing about the 1200, is that it is backward compatible with older programs by pressing the two mouse buttons before turning on the computer and using the options to get an "older" chipset that some programs need.
If you can't get that, A500's and A2000's are still widely available on the flea market circuit, and will do you fine for playing games, although you can't try one's that designed for AGA, but tons of games were programed for the older systems, so you'll be busy for a long time with the older stuff. It helps if they come with a HD already.
Have fun.
