Hi Fred. I agree with what Argus is saying about the A3000. An unexpanded system already has good features available, and it also has good options for further expansion, and will generally give good value for money.
I don't know how aware you are of the Amiga graphics chip sets. The original chip set was called OCS, and was later upgraded to ECS. IIRC, both of these chip sets had essentially the same behaviour with games (someone please correct me if I'm wrong). Most Amiga games were developed for OCS/ECS. I think any Amiga can support the screenmodes required for these games. Later, in 1992, the AGA chipset was introduced, and was featured in the A1200, A4000, and I think some European (or German) only model(s) like the A2200. AGA has superior graphics capabilities, but there has not been a large amount of software written which requires AGA. Having said that, some AGA games do look fantastic.
There are also additional graphics cards for Amigas, though not always easy/affordable to get a particular model that one may desire. These cards offer superior graphics output, and faster performance. Others have said that they are basically essential for web browsing these days. Also, I've read that some newer (post '96?) games require graphics cards and 3D accelerators. I believe some graphics cards will allow AGA Amigas to pass the AGA screen modes through the graphics cards, to still be displayed, whereas some would not allow this. It should be easy enough to fit a graphics card to an A2000, 3000, 4000, 2200?, but more difficult with other models. With an A1200, if you don't have a bus-board expansion, providing extra slots, then I think there is only one graphics card available, BlizzardVissionPPC, which is only usable with a BlizzardPPC accellerator. I'm not sure of what other issues may be pertinent for the use of graohics cards.
You will also want to know about scandoublers/flickerfixers. Most games work on a ~15kHz scan rate, which is too low for most modern svga monitors. Scandoublers/flickerfixers will promote these screenmodes to be displayable on your monitor. I believe the A3000 has one built-in, which is great, as add-on SD/FFs can be expensive, don't always work very well, and can be hard to find (though external SD/FFs are currently commercially available).
There is a couple of other compatibility issue to be aware of. Some software is not compatible with 68040 and 68060 CPUs. For most Amigas, these CPUs are only available on accelerators, though some A4000s shipped with 68040's. Accellerators can generally be disabled when required. Additionally, you should be careful of which ROM's are installed on-board. For OS 3.1, 3.5, 3.9 you need ROM version 3.1, though OS 3.1 will run with limited features using 3.0 ROMs. However, some games may want to use earlier ROMs, like v1.3. This is not such a major issue any more, due to a program called WHDload, which allows old floppy disc games to run from hard drive, and I think eleviates the issues with ROM compatibility. If I remember correctly, this now works with most games.
You mentioned that you don't know what accellerators are. They are cards with upgraded CPUs, faster clocks, more RAM, and possibly coprocessors, or memory management units. They may also feature IDE or SCSI interfaces. Accellerators are truly good things to have, though they can cause some compatibility issues as mentioned above.
Have fun, and good luck.
-Oli
