You should never, ever, buy a used 360 unless it comes from someone who can be trusted.
For one, the console might be banned from xbox live. Then of course is the warranty issue - at least the european repair centre doesn't acknowledge the 2nd-hand market and you'll need the original owner to deal with MS to send it for repairs. Of course, the fact you might end up with a broken console with expired warranty a few months down the line should bother you as well. Repairing the console out of warranty is like 80-100 dollars so it'll eat whatever savings you made on the used console.
edit: since you are on a budget, I'd give blue dragon and lost odyssey a second look, you should be able to find them pretty cheap.
Current-gen game collection uploaded on the profile, full of win and good games; also most of my PC games. Lucasfilm Games/LucasArts 1982-2008 (Requiescat In Pace).
