If you are going to buy one, get the one with the Intel core duo in it. This is the one with two cpu cores packaged on a single chip.
There are other versions that you need to be aware of:
1. PowerPC G4 - this is the old one. Avoid if possible.
2. Intel Core Solo - newer, but with only 1 core (as opposed to 2).
As far as I can remember, the mac minis still have integrated graphics built-in which uses system memory (as opposed to dedicated graphics memory), so you may have problems playing the latest games..if that's what you're into.
The new Core Duo should be plenty fast... however, it all depends on what are going to do with it.