Technically you could probably just provide more active roles / personalities for the women already present in the original crew, as Abrams did (to some extent) with Uhura. The original series was hardly lacking in women, it just put them in mostly minor or passive roles.
But that comes at the price of whining about what happened to Chekov or Sulu when Chapel or Rand take the screen time. People come to expect certain roles to be in place, which is why the movie has Chekov coming in, however improbable. General audiences don't care about Number One or Boyce either, they just want the core people, which is why that issue is difficult.
Updating the futurism -- and leaving behind tropes that started out as budget conveniences in early Trek before calcifying into traditions -- would be a major necessity.
I think that updating it to any real degree sort of nullifies the way things turn out. The creation of uber smart AI (which will likely precede interstellar travel) brings up questions of the technological singularity.
And let me say that this isn't necessary, but it would be nice. People aren't going to be wowed by ideas of androids, padds, or replicators.
that doesn't necessarily mean going in for "stereotypical anti-heroes" (which I suspect television audiences are ready for a break from, much as I love Breaking Bad and Game of Thrones and House of Cards) or entirely abandoning episodic story-telling (which is still done well, if on a more sophisticated level today than in the Sixties) and drives a number of popular shows.
Even the most episodic shows have growing relationships and life changes that happen, which Star Trek practically had none of. The later shows had more, and even DS9's quasi arc story format I think audiences would prefer to standalone stuff.
And I don't think antiheroes are going anywhere. The sort of comic book good vs. evil stuff just doesn't fly on TV anymore. Everyone is flawed, and that parallels real life, which helps people identify. The Abrams films have done well in dropping the flaws in to Kirk and Spock, but there may be a desire for it to go further (although not Admiral Marcus far).
As far as the comments about militarism, I think that the shows want to have a more lax approach to appeal to the common viewer. Typically the person who is strict and rigid is a trope that shows us they're not like our heroes. Anyone who is by the book or all about procedures will seem stuffy and people will want to not like them.