I've been thinking about this one.
As much as it pains me to say, I would probably go with the PS2. The system itself is more expensive, but a lot of the good games are inexpensive (as long as you don't want the newest stuff) and it's backwards compatible with PSone games. Plus, you can play DVDs on it. If you're a poor cuss, the multifunctionality is probably a good thing.
But it does seem like you're leaning towards a Gamecube, and if you like Nintendo's franchises, why not get a Gamecube?
If you end up getting a Gamecube, there's a lot of good games that you should be able to get for $20 or less. Here's just a few of them:
Legend of Zelda: Wind Waker
F-Zero GX
Sonic Mega Collection
Sonic Adventure DX
Sonic Adventure 2: Battle
Sonic Heroes
Super Monkey Ball
Super Monkey Ball 2
Metroid Prime
Mario Golf Toadstool Tour
Resident Evil (aka "REmake")
Resident Evil Zero
Super Mario Sunshine
Viewtiful Joe
Splinter Cell
Namco Museum
Midway Arcade Treasures
Midway Arcade Treasures 2
Soul Calibur II
Billy Hatcher and the Giant Egg
Luigi's Mansion
Star Fox Adventures
Animal Crossing
NBA Street V. 2
Harvest Moon: A Wonderful Life
Lord of the Rings: Return of the King
Skies of Arcadia Legends
Metal Arms: Glitch in the System
Second Sight
1080* Avalanche
Pikmin
The Sims
The Sims: Bustin' Out
And there's even more than that if you count sports games and used games.
(**Bolded ones are ones I personally own and can attest to them being pretty good games.

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