Since CBS just announced that there's another Star Trek series in the works, I'll take a moment or two to put my particular thoughts about Star Trek as a franchise and as a headcanon in one place so that I can just refer to this rather than trying to remember what I need to type out whenever the Star Trek discussion comes up again in some thread somewhere.
Here's what I think the perfect Star Trek show is about: cooperation in the face of cruelty, diversity as a given rather than some sort of quota or question, diplomacy as a powerful solution, and violence as both a last resort and an acknowledgement of failure. I want to see, basically, The West Wing in space, where fantastically intelligent people from radically different backgrounds are fighting with all of their brains to prevent terrible things from happening by talking very, very fast and using extremely big words, all of which are currently available in a dictionary.
I have a personal belief, based on my experience mostly with the Star Trek Online game, that the various bits and pieces of information about Starfleet are effectively all hogwash and propaganda -- that Starfleet isn't the cremé-de-la-cremé as Krugman et. al. profess, but rather it's a makework jobs program for the misfits and the weirdos. Basically, in STO, since the given player's skill level is unpredictable, the lived experience at that point is that anyone who wants to be in Starfleet gets to be in Starfleet, regardless of their actual skill level or aptitudes. We even see a little of that confirmed in canonical sources like DS9, where some of Chief O'Brien's staff are not exactly the "best and the brightest" (or, for that matter, some of the non-coms even on the Enterprise in TNG aren't exactly the sharpest knives in the drawer).
Note that I actually like this model of Starfleet / UFP. Basically, the idea being that if you just want it hard enough, the bureaucracy will find a place for you, and will do their best to utilize whatever skills and interests you are interested and invested in bringing to bear. A true meritocracy, where what matters most is a willingness to try and a commitment to being part of something greater than oneself.
That's the story I want to see told, the series I want to see filmed: that people (of whatever shape, size, or system), working with will and commitment, can build something amazing and lasting and sometimes galaxy-changing. Together.