I own a Gamecube, my brother has an X-Box.
For extreme graphics, dvd's, and large title selection, go with the X-box.
The PS2 has the largest title selection(I think), but the graphics aren't on the level of the X-Box.
Gamecube has good games and good graphics, but does not have the title selection that XBox and PS2 have, and it can't play dvds. The only true upside is the fact that you can get a Gamecube for less than half the price of the other two systems, and the games are cheaper(usually). If you get a Gamecube you have to have Zelda Windwaker(the best Zelda yet, even better than Ocarina), Mariokart Double Dash, and LOTR Return of the King is pretty good on Gamecube but is probably better on Xbox.
And if you don't like how the Zelda series has contiually gotten more and more kid oriented with each release, a new Zelda game is coming soon that is more adult oriented(Link is grown up) and it looks more like an action game.
Hope that helps.