The GameCube really is a pretty awesome console. I find it more fun to play than either my Xbox or my PS2. I just bought a new one a few weeks ago to replace the one that got destroyed (luckily, all my games survived)... it's great.
Super Mario Sunshine really isn't all that hard, it just takes some getting used to. Once you master the camera, you'll be fine. Take your time and explore a lot. I have like 14 extra lives now and I think three shines.
(You can get a GameCube/Sunshine bundle for $189, which saves you $10, but you'll also want to get a WaveBird as well. I'm told you can find these for as low as $25 if you shop around, but expect to pay $35. It's a great controller. Lastly, you definitely want a memory card, so $20 there.)