It seems to me that each of the 3 races will match up with an individual class. Humans seem inclined to be Hunters, Exo seem to be Titans, and Awoken seem to be Warlocks. Obviously this isn't, like, locked or anything, but just based on what I've seen of the characteristics of the races and classes those are the matches I would guess.
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According to the team at GDC, there will be no difference in how each class plays due to race. The race is just whatever you like the look of best.