The Amiga had various chipsets over the years. The major variation deals with Graphics.
OCS is the original chipset.
ECS is the Enhanced chipset, essentially it's exactly like OCS but it has a few 64colour screenmodes called "Extra Half Brite". Essentially it took the first 32 colours and then dimmed them to half their intensity.

A500's had either OCS or ECS.
AGA is the Advanced Graphics Architecture (AFAIR). It allowed for screen modes of up to 256 colours, and HAM8 mode would allow for almost true-colour graphics (instead of HAM6 which gave you 4096 colours). There were a few other upgrades, but essentially AGA had more colours and more screenmodes.

AGA were used in Amiga 1200's, Amiga 4000's and CD32's (oh, and those Index Access computers.)
AGA is fairly compatible to ECS/OCS, and in fact you can boot your AGA systems into ECS/OCS, but some games still had some compatibility issues. To make matters worse, all of the AGA systems had 020 or better CPUs which caused more problems with incompatibilities.
So, if you're really into playing older games, you might want to have an A500, KS1.3, extra floppy, 512megs of ram with the slow fast ram.
For the AGA games an A1200 is pretty decent out of the box. And it can use your A500's monitor, joysticks and extra drive. The A1200 already has 2 megs of chip ram, so most games should be happy.

Oh, almost forgot, some of the newer "Escom" era A1200's use a modified floppy drive which might not boot any of the older games.

However, a lot of the newer games require a more powerful CPU, harddrive, CD drive and more ram.

Confused yet?