I want to see a disabled captain who tries to run over everybody with his wheelchair.
Perhaps one of the crew (Captain) can be a Stephen Hawking.
Also having a character an alien immediately gives them a distinctive look and perspective on things
The different perspective aspect would be nice, and while they are being aliens lose all the "half-Human" characters. And don't do what they did on DS9 with the Ferengi and turn them into nice little western civilization Humans at the end.
If there is a episode that features the federation council, try not having it be basically a version of the "West Wing." There are a hundred and fifty alien races, each with (likely) multiple cultures, have the writers show some imagination in how things are done in the council.
TNG did a fairly good job (initially) of not showing Vulcans, the new show can continue that theme with not having the same old tired list of establish aliens - except maybe on very rare occasions. No Klingons, Cardassians, Andorians.
And please God no Romulans at all.
On the other hand, some of the races we've seen, but not too much of, could be explored. For example we never really learn much about the Tellarites, the Bolians are semi-unknown, is everyone one from Risa a resort worker - or do some of them reject that occupation.