Thanks for the recommendations, guys.

I'm 50 stars into Mario 64, and I'm honestly not sure I want to finish it. I'm torn over how to feel about the game.
On one hand, there's a lot about it that's completely amazing for its time, and its clearly the work of some genius game developers.
On the other hand, I spend a lot of time yelling at the TV because of the control and the camera. I've gotten much better at the game in general, but the control is still something I have to "deal with", not something I can take advantage of. Instead of developing a sensation of direct control, I feel more like Mario is a ball in a pinball machine and I'm just working the flippers. Maybe that will come around with time.
I'm thinking it would be fun to play another 3D platformer-ish game that came out some relatively short time later and has a better camera system/control. It could help me appreciate the evolution of 3D game development, if nothing else.
If I ever come across a cheap Gamecube, I'll buy it. For now, maybe my Dreamcast is where I should go next.