Crash Team Racing is the pinnacle of kart racing games. The driving is more skill-based than the leading brand name, and it doesn't have shitty rubber-band AI.
Star Wars Episode 1 Racer is still great fun, easy to learn but hard to be good at.
Nothing compares to F-Zero GX. The abandonment of the franchise is a travesty, and should be considered abuse of the gaming community.
Pro Controller at the very least. CTR is a game that should be played with a dpad for steering. You can use the analog inputs but some more advanced tricks (such as tight steering) will require a solid dpad.