I really like the idea of making the crew be more fluid and/or bigger and getting away from the idea of having 7 main characters and sort of trying to fit them all into boxes leftover from TOS.
I also think that if Trek is going to come back to TV it should take a page from Doctor Who and other "genre" shows and have shorter seasons and one arc connecting each episode. Twelve or thirteen episodes seem to be the norm for shows like Who, Walking Dead, True Blood, etc. It would save the budget, maybe attract bigger named actors to commit to the show even if just for a few episodes and make every episode count. No filler. They can still go to this random planet over here to settle some kind of dispute or investigate this anomaly over there, but there should be something pushing the overall plot ahead. I think this would also keep them from falling into some of the same cliches that past series did.
I had forgotten, until I started rewatching over the summer, that TNG seemed to attempt this during season two by working hints about the Conspiracy plot into episodes throughout the season leading up to Picard's confrontation at Starfleet. I don't know why they seemed to abandon this later in the series. It doesn't have to be as frantic as The Walking Dead or as big and heavy as DS9's dominion war, but I think having each season set out to tell one story in an overall bigger story would be ideal and hopefully keep people interested.