Nintendo always puts out the most durable products. I still play my NES, I got it for Christmas when I was five. Things with MS involved usually break down, like my computer and my Sega Dreamcast. The Xbox is the same. The PS2 only sales so many units because everyone that buys one ends up buying a second one. After you buy a bunch of games for your PS2 it dies leaving you with a worthless library of software unless you were to go out and buy a PStwo.
The GameCube is most likely to not break down of the three disk systems, plus you can get the GBA player and play GBA games for cheap on your tv. The bundle is a great deal, but don't forget to pick up some kind of memory card, even if it is one of the smaller cards.
You get Mario Kart Double Dash which is probably the best multiplayer game that anybody can pick up and play. The GameCube has the best lineup for families, I don't like to say its for kids because it is for everyone. The Legend of Zelda: The Wind Waker, Mario Party, Mario Tennis, Mario Golf, Pikmin 2, The Sims, and many other games that are already out for the system may appeal more to your kid than the frat boy games available for the Xbox and PS2.
The GameCube is also still going to get some killer games before the next system is released. The best game of all will most likely be the next Legend of Zelda which comes out next year.
I would go ahead and get the Cube now. The price might drop some during the spring, but you never know when. Best case scenerio, you get the Cube now, buy some games for it, then the next system comes out in 06 and is backwards compatible and able to play all of the Cube games you'll alread own. Worst cast scenerio, you get the Cube, the price drops fifty dollars in Jan. or Feb., the next system is released in fall of 05 for $250 and isn't able to play Cube games.