Dru's opinion: it depends.
I own all three systems. I have a HDTV, and I have two kids (4.5 and 7.5). We have DDR pads, and several versions of the game. We also have Kongas for Donkey Konga and Taiko Drum Master, among other things.
Technically, the Xbox is the superior platform, on a hardware basis. This, however, isn't terribly relevant to actual usage, as often as not. Most consoles are worth selecting based on the quality of their exclusives, or features that appeal to you.
ALL three systems output to HDTV. 90% of Nintendo's 1st-party titles can be displayed at 480p widescreen, as can most X-box games. Some PS2 games can do this, but it's not a widespread feature, and Sony's support has been poor. It should be noted that while the Xbox can do 1080i resolutions,
very few actually do. KOTOR and Halo2, for example, are 480p only. Xbox support of HDTV is much better implemented overall, however.
The gamecube lacks two features the others have: network connectivity and DVD playing. How important these features are is up to the individual. Both the Xbox and PS2 aren't very good DVD players, and I NEVER use mine for that purpose. When the PS2 was new, this was a great feature, but many DVD-players are now cheaper than most new games (and that's not factoring in the cost of remote control module for either unit). PS2 online gaming is clumsy and inelegant compared to the Xbox. Xbox live is a thing of beauty, and a reason to buy the system....if you like playing online games, that is. Xbox also offers downloadable extended content for many of it's games through Live, as well, which is a nice feature, too. For those so inclined, Xbox is also the best unit to hack and turn into a DVR or what have you.
What Gamecube does have, however, are some of the best games for a family environment and the single best wireless controller EVAR. The 'cube also has some excellent pack-ins, is much more portable than it's competitors and is the least expensive of the three (and has better support in Japan than Xbox has, by a wide margin). The cube also has the most party games of any console, if you like that sort of thing (and I do). While we're on the topic of games, btw, the 'cube also has some of the best 'I can play with my kids or with my kids in the room' games. It will be nicer when some more imports (such as the Naruto fighting game) make their way to these shores.
PS/2, of course, has the most games, bar none, and backwards compatability to boot. It's got the most sold units, which means the easiest to get third party products and software for. It dominates some categories (such as console RPGs, arcade fighters, tactical games) and has solid contenders in every category. It has more beatmania games (such as DDR, Para-para and so on) than the other two by a huge margin. A nice bonus is being able to buy some of the console's best titles from the past for a pittance, such as Metal Gear Solid 2 or Devil May Cry for a mere $6.
If DDR is your consideration, I would recommend the PS2. Xbox really only has DDR Max to work with, while the PS/2 has both the PS1 and PS2 DDR games to choose from, which gives you the most songs and widest variety. I HIGHLY recommend the Disney version of DDR, for a good song selection, excellent tutorial mode and selectable skill level. Regular DDR is brutal, IMHO, and not a good beginning point for someone new to the series.
I hope you're on the ground floor, by the way, as jumping on DDR pads will sound like herding elephants to people beneath you. Take the word of one who knows.
Ultimately, each system is well worth your money, depending on your desires. There is no wrong answer, just the best choice for you. Give us some more specifics, and I'd be glad to offer more advice.
but it is far better than the PS2 controller... 
A serious disappointment on an otherwise fantastic wireless controller (makes playing Zelda... not fun). But that's just me - I've been entirely spoiled with controller force-feedback, and won't go without anymore (especially as more games are including it as a gameplay feature).
