If it is anything like Mario Kart 7, then stats will be applied per weight class, not character.
They've ditched two weight classes; feather and cruiser. Light, Medium, Heavy are the three.
Knowing Nintendo, Heavy will be best for Time Trials, and Light will have advantages online.
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There is a rumour going around that the ability to freely vote courses online has been changed.

The above image is from the direct; it displays when talking about Worldwide functionality.
The player has a choice of three courses to pick from, or to pick random.
(Which I assume would randomly select out of the three offered)

This screen follows immediately after.
Here you can see that all 12 players are voting the same three courses, or random.
I'm guessing this is Nintendo's solution to halt people who repeatedly vote the same courses.
Although, if this is also a prominent feature in Friend Rooms and Tournaments...
It may turn some people away from playing.
I expect the worst from Nintendo because of their previous installment—hopefully this isn't forced everywhere.