Classic Amiga computers use a set of special (Amiga-only) Chips, the so-called "Custom Chips". There are three major revisions of that custom Chipset:
1. OCS ("Original ChipSet")
2. ECS ("Enhanced ChipSet")
3. AGA ("Advanced Graphics Architecture")
The Amiga 500 (the most popular Amiga model) either has OCS or ECS, hence most games will work with OCS/ECS.
The A1200 (the A500 follow-up) has AGA, and it was still a pretty popular machine - that's why there are games that will require AGA (the
Hall of Light lists 245 AGA games).
The best machine for gaming? Either an A500 (will run (nearly) all OCS/ECS games unchanged but will not run AGA games) or an A1200 with an internal Harddisk and some additional Memory.
The latter setup (A1200) will have problems running many OCS/ECS games properly, but you can use
WHDLoad to install all your old games on your HD. WHDLoad will also kill all compatability problems (OCS/ECS games on AGA chipset), but it requires some additional RAM.
There are a bunch of newer Games (about 30-50 I'd estimate) that will require a more powerful machine than a stock A1200, but upgrading an Amiga to play these (many of them are "just" PC ports anyway) is damn expensive.
