I want to see the filmmakers do whatever they wish, with no regard for the "fans", unless it is what they want to do anyway (of course, I want that from every form of artistic production). I do NOT want to see them cater to any particular agenda in order to please the self-appointed guardians of The Committee for the Way Things Ought to Be (patent pending). Any agenda should be entirely of their own choosing.
A story revolving around some sort of mystery--finding the remnants of a lost colony where it shouldn't be; encountering previously unknown technology, which attracts the attention of the Klingons generates some action/conflict but also forces them to work together to solve the mystery (maybe some sort of cliffhanger for a fourth film?); or maybe have a story inspired by something that's mentioned as a throwaway line in a TOS episode (have that be the wink/nod) and then develop the "adventure between the episodes" without having to be slavishly faithful to the prior or subsequent episodes in any way.
As for what to do with the characters--Kirk and Spock should remain in centre stage (they are by far the most important and interesting characters anyway) and there should be no time devoted to others at Kirk or Spock's expense (Want more McCoy, or any one else, this time out? Cut down on someone else--just not Kirk or Spock).
Otherwise, as I've thoroughly enjoyed Bad Robot Trek so far, I feel quite confident to let them handle things for as long as they want to.