You should get the program Mactracker, which gives details on all the models in order of their introduction, along with the codenames that they are usually referred to by.
The current latest version of OS X, 10.4 Tiger, is great and runs on any G3 or above Mac (you need to use XPostFacto to make it install on a Beige G3, while it will install more easily on a Blue & White or other colourful G3, but don't be put off as once you've got the installation itself done it's no different to running OS X on a "supported" Mac). The next version, 10.5 Leopard, will only run on G4 and above. Don't let anyone put you off the Beigeys, they are great machines and I love mine! (my first and only OS X machine!)
Better still, you should be able to pick one up for free without too much trouble (B&W G3s can also be found for free but are rarer, whereas G4s are expensive still).You'll want at least 256 MB Ram, and preferably 512 MB or more, whichever Mac you get, if you're running OS X. You'll also want a reasonable video card - a requirement on the Beige G3 as it's very difficult to get OS X set up using only the integrated video, and a good upgrade on the B&W G3 and later as the stock video card is not good for OS X performance. A Radeon/Radeon 7000 Mac Edition shouldn't be too costly (note that PC cards are not compatible unless you want to get into flashing them, but even then I think the real Mac Edition cards tend to work better). For hard drive, it depends what you want to install on the machine - a few GB is enough for an installation of Tiger, but you should be able to find a nice 20 or 40 GB drive at little or no cost though.