Well, there's been a 5e concept based on Leadership (I reposted my entry as a separate thread), which had a class version. You probably don't need to post these interest checks, as you can just make a chat thread and work out the contest from there, much like the long-running 3.5 class contest has.

As for a theme for the first contest, you could go with Deals. Pacts, bargains, contracts, whatever synonym. This would likely result in a bundle of Pact Magic classes, most likely, but that's honestly a good thing because Vancian gets seven classes in 5e, with five that aren't Vancian, and Pact Magic classes are weirdly close to nonexistent in homebrew.