What kinds of characters would you like to see?
I'd like to see TOS-Era adventure -- now that the notion has been opened up by the "reboot," a good thing whatever one thinks of the BadRobot films -- that doesn't tiptoe timidly around in the shadow of Jim Kirk, but explores the adventures of another Constitution-class ship of the era on its own terms... and has a roster of characters conceived for that purpose.
I like aliens but I'm not especially fond of the idea of significantly upping the alien quotient: we still have a ways to go with exploring human characters in this setting as it is. I would like to see:
:: A Captain with some depth, but whose character draws on heroic archetype as successfully as Kirk's did. Kirk was a (very iconic) Horatio Hornblower analogue; for a different but equally vivid archetypal grounding I'd look toward an Arthurian-knight-born-out-of-his-time idea (a widower who doesn't seduce his way out of trouble, a man of sternly-held honour who tries not to resort to deception and treats even enemies with grace, equally capable as a soldier and a diplomat and with a strongly-implied spiritual side to his character [but not crude religiosity]).
:: A Science Officer who is not "the logical one," but represents the exuberant, intuitive, humorous, fly-by-the-seat-of-your-pants side of science that's about joy in discovery. It would be nice to have a straightforward human in this role for once, frankly, given the extent to which Starfleet is powered by human science... but I also quite love the idea of a Deltan science officer with a silk-hiding-steel kind of character vibe.
:: A Helm Officer as a Lt. Commander and Second Officer, since it makes zero sense to keep calling the Chief Engineer away from the vital systems to perform this role. I would love for it to be a character that was everything Sulu should have been and was never allowed to be: a forceful personality, a frequent major player in command decisions and saving the bacon of more senior command, a joyful swashbuckler and an openly gay man or woman (gender doesn't really matter).
:: (A fondness for
Firefly creeping in here, but there were at least plans to include Ship's Chapels on the
Enterprise) A Ship's Chaplain in the "counsellor" role, which will probably sound a touch nuts but does make a certain amount of sense as a) a signal of religion's having made its peace with science and progress, b) sects of human faith integrating the knowledge of discplines like psychiatry and learning to speak to each other and to secular people with maturity and goodwill, and c) a making-explicit of the implicit religious and hieratic imagery in which the series is positively drenched. The conscience of the ship and the guy (or gal) who talks the Cap down if he loses perspective. It would be fun to make them a tough-as-nails former prizefighter type (or whatever is the closest analogue the 23rd century has to prizefighters), and also the ship's historian (to provide a reason for them to be on away missions).
:: An avuncular, fatherly CMO played by Morgan Freeman. (Okay, jokes, but someone who captures that kind of centered, seasoned, mildly-amused, utterly calm and confident energy.)
:: An amusingly cantankerous and frighteningly competent Tellarite engineer. It's always bugged me that the Tellarites get no love.