What I'd personally want to see:
not a reboot. Whether one qualifies the previous new shows following on from TOS as "not reboots" or "soft reboots", those
are fine. All they really did was take the existing universe and create a new story IN it set farther ahead in time. I'd much rather see something like this, where we run with a brand new set of characters and ideas, than creating the third
version of the Kirk/Spock/Enterprise story. I'd be more enthused about a TNG animated reboot than a TOS animated reboot, partly because it hasn't been done and partly because I prefer 24th century Trek anyway, but my #1 choice is still something entirely new in terms of the characters and stories. The only "reboot" aspect I'd want to see is perhaps making a clean break in terms of the setting - rebooting in the sense of what nuBSG did, where there is no in-universe connection to the old setting. They are too entirely different entities spun from the same base concepts. But, unlike with nuBSG, I still prefer the idea of the characters in a new Trek series being entirely new (and the ship not being "Enterprise", while we're at it).
Animation-style wise, pretty much a semi-realistic look would be my first choice, either as full CG - i.e. something along the lines of FFVII: Advent Children - or a kind of CG-with-cel-shading-so-it-looks-like-2D look. I think the tech and capability to create high-quality CG animation for a weekly show is already here, as evidenced by stuff like Transformers: Prime (which is also a good example since a lot of the main visual content is sci-fi in nature): http://www.youtube.com/watch?v=cXxmMW5USHg
Personally, while I'm certainly not trying to impugn their quality simply as art
(they're definitely well drawn and are obviously intentionally very stylized),
I'm not as much a fan of either of the examples posted by milojthatch,
when thinking about the kind of look I'd want for an actual Trek show.
I would combine a brand new set of characters with animation like I described above in a serialized, arc-based story with a very serious, modern treatment of the Trek setting - more DS9 crossed with some stylistic and tonal elements of STID, and less TOS or TNG, in terms of the overall tone and feel.
What is most likely to even be made, let alone be successful:
I fully acknowledge that what I'd personally be most interested in seeing (or would make
, if given the opportunity) and what is most likely to be made and succeed as a Star Trek production, are two different things. While I generally like the Abrams films for the most part, I'm tired of Star Trek "being" Kirk, Spock, and the Enterprise. Yeah, it's the most popular part, I'm not saying I don't understand that, just that I think it's a shame that - outside the novels - this whole huge universe is being ignored in favor of obsessing over this one set of characters over and over. I also feel that another Trek series that examines politics, morality, war, and other such weighty subjects to anywhere near
the level that DS9 did is a near impossibility, despite that it's what I'd most like to see.