Chemist could be interesting and make him super smart, although it might be falling into line of a lot of other random comic book characters that are scientists or whatever, which might make it less unique. Definitely agree that it would be nice to not get the clown/comedian/military thing again.
I'd really love it if they just never explain what he is, he just shows up one day and is the true wildcard to the criminal world in Gotham, everyone is afraid of him - including other criminals and gangs. In TDK he works with them (I know he has his own plan and uses them, but he still has ties to them and talks with the mob) but in this maybe he's truly just on his own? I love the TDK force of nature idea, but remove any of the hints about a backstory entirely. I also don't really dig when Joker becomes super deranged like in Scott Snyder's Endgame, for example.
That's probs what I'd like to see (but I'm down with most directions tbh). I don't really find Joker as a character interesting at all, the interesting bit for me comes out of the moral positions he puts Batman in, so that's why I'd prefer no backstory at all and he's just straight up plopped there, current gangster, anarchist or not.