Before Beyond I wanted to see the Federation finally clash with the Klingons... and see how Kirk and co react now that they took the Vengeance off the table. Beyond went, well, beyond expectation. So I don't really know what I'd want to see plot-wise. What can you mine from the original series that is deep enough to expand into a movie plot? Sure, the Doomsday machine is there, but I'd like for something more interesting.
I do agree that Id like to see Justin Lin come back to direct and Pegg with Jung on the writing team. It's nice to see so many trek fans happy with Beyond where there was outrage against the new movies in the past. This crew did it right, and I'd like to see another Trek film by them.
I would also like to see the A put up a successful fight. I do wonder if they haven't had the Enterprise hold her own past 2009 because "fighting in Star Trek is BAD!", but c'mon, a lot of fans are like me and love the hardware. We want to see the new A hold her own against hostile alien forces.
Perhaps for 4 they could bring back the godlike energy beings we haven't seen since Q. Maybe like the Metrons, some being to throw the crew into a perilous situation to try understanding why mortal beings like the crew are so special.