What I really look for in a Mario Kart game is the tracks. I really loved the ones in the Wii version, so that made it more enjoyable for me.
Basically I want great tracks (like the DK one from the GCN version, I always found that one to be so much fun), better item balancing than in the Wii version (so - literally - being hit by six items all at once in front of the finish line on the third lap and losing a race you had easily won't happen), and, of course, graphics that really take advantage of the Wii U. I know... Graphics... Who cares about those? But I think that Mario games can look great in HD. I have a feeling Mario Kart will be underwhelming in that regard, though. The Wii version seemed a bit off graphically to me.