There have been a couple responses here putting down the gamecube. Its only real fault is not embracing online play. It can't play DVD's either, but personally I don't find that to matter all that much.
The real way to pick a console is to look at the games out for it and decide which games you prefer.
PS2 has by far the biggest library, but there are also more dingers in there because of that, though still plenty of good titles.
Xbox has a few good titles but caters more to adults in my view, though that isn't a bad thing. Xbox aside from Halo doesn't seem to have many gotta have titles.
Gamecube has been overlooked by many but has a well-rounded library. Certainly those who like Metroid, Zelda or Mario will much prefer Gamecube. There are more kid games, but there are plenty of other games as well. The only thing is lack of online play and some developers don't put their titles on the Gamecube because they feel it won't sell as well there.
Of course I own a Gamecube so lean towards it. The other machines are good as well though and as I said I think a decision should be based mostly on the kind of games you like more than simply which is the most powerful graphically. Also I prefer the Gamecube controller over the other controllers. One other advantage the Gamecube has is its cheaper than the other two systems.