If you know that you're going to go into this professionally, then I'm inclined to agree with nebula_42 that you should buy pro-grade equipment out of the gate ... assuming you can afford it (if not then at least you should buy the best you can afford).
If you're not going to go into this professionally, or are not sure about it, then the choice is less clear.
Buying new gets you the warranty and while that will give you some peace of mind, you do sacrifice something for it. In this case, the 20D is a significantly better camera than the 350D (a.k.a. Rebel XT). Reportedly, the 20D's autofocus system is noticeably better, particularly in low light. If you're looking to expand your horizons as much as possible, you'll want the camera to limit you as little as possible, and that argues for the 20D (or even a 30D if you can swing that).
I suspect the best way to minimize the chances of getting a dud 20D is to buy it from one of the people in the POTN market forum. Buy it from someone who has been a POTN member a while and who has racked up a number of messages, and chances are better it'll be someone who can be trusted (mainly because you'll at least know that they're not here only to sell their stuff). You can even look over their previous postings to see what sorts of things they talk about, if you want to get some idea of that sort of thing. There are no guarantees, of course, but there are things like that you can do to maximize the chances of a satisfying purchase.
Keep in mind that you'll need lenses as well. There's a lot of good advice on these forums about what lenses are excellent and what lenses to avoid. Some lenses, such as the kit lens, can be had for amazingly little money and are surprisingly good (see my sig for a link to a thread with some impressive pics taken with the 18-55 kit lens).
Good luck, and don't be afraid to ask questions! We're here to help.
EDIT: one more thing: you should go to a store (like Circuit City, Best Buy, or your local photography store) and handle both the 30D and the Rebel XTi. Those two bodies are almost identical to the 20D and the Rebel XT, respectively. If you find that the XTi is too small for your hands (as I did) then you'll be quite unhappy with the XT for that reason alone, even if it would otherwise meet your needs. That kind of issue would be a very good reason to go for the 20D despite the lack of new warranty.