The biggest stretch for me would be race rather than class. I've always played either casters or rogues, human, dwarf, or pure elf. But if I get to play I'm looking at Half-Elf Warlock. I used to roll my eyes when people would choose half-elves in the past, but mechanically and story-wise I think I could make it work and even enjoy playing it.
I'm thinking about a half-elf raised by his human father, who was a wizard of some minor power and influence locally, determined to make sure that his son studies to become a great wizard (sort of like the lunatics that push their kids in sports, cheerleading, and other quasi-competitive areas to relive the 'glory days' that never were.) The half-elf is bright, but not really all that enthusiastic as a scholar. So he finally makes a pact with otherworldly beings for arcane power, just so he can say, "Look, I'm a powerful wizard" to his father, who honestly wouldn't be able to tell the difference. Except now that he's there, he's satisfied his father's wishes, he has no idea what to do with himself. No one ever asked him what he wanted to do. Plus, he's got all the weirdness that comes along with having made a pact with otherworldly beings. Half-Elf Star Pact Warlock with wizard multiclassing. If half-elves get the multiclassing feature as good as or better than what's in the fan-collected preview material. Alternately, a human warlock with a similar story, just less multiclassing, perhaps just some extra skill training.
Second choice, Dragonborn Rogue. Trained by his people to locate and recover artifacts from the ancient, fallen Dragonborn empire, to ensure that their cultural heritage doesn't fall into the hands of tomb robbers and collectors from other races. Perhaps part of an order devoted to Dragonborn historical / cultural preservation, they wouldn't just raid the tombs and ruins of the past DB Empire, they've also been known to track down tomb raiders from other races and slip a dagger between their ribs, and reclaim the items which have been 'stolen.' A thief/assassin type who sees himself as neither thief nor assassin, but a defender of culture.