I'll say what I usually say about what I'd like in a Star Trek movie:
* No Earth, and preferably no Federation contact. So far, the only film to come close to this was Insurrection. Beyond had Yorktown as sort of a stand-in for Earth in terms of the stakes.
* Perhaps more of a look at either civilian life or an alien civilization. The teasers for the past two movies actually seemed like better premises for stories than their respective films. I'd love to see a movie about Nibiru, or a movie about Kirk learning diplomacy on the job and a more direct look at the consequences
* No villain, though an antagonist that eventually meets the crew halfway
* No death and little to no destruction, I think this would be a challenge to the writers to see if they can solve the puzzle of the story without resorting to death
* A lower budget, definitely under $100 million. I wish they wouldn't chase the summer tentpole audience, but instead chase the fall hard sci-fi audience.
* An ensemble feel, I think Beyond was a step in the right direction, though TVH was probably the pinnacle of that kind of storytelling
* A focus on problem-solving, again Beyond was a step in the right direction, while TVH was the pinnacle
* An anthology format, I tend to think this is an ideal format for adapting any TV show honestly (I think that if they make another Simpsons movie they should do something like 22 Short Films About Springfield), Judgment Rites, A Final Unity, and Master and Commander are models to look at for this style of storytelling
* The writers should look to the following films for an influence on tone: Close Encounters, ET, The Abyss, Tremors, Contact, Master and Commander, Gravity, Interstellar, The Martian, Arrival