Personally, I'd want a series set around 2462 aboard an
Enterprise-H. I'd like it to be a bit more daring than previous Trek shows, while still retaining a sense of fun. I'd like it to have a smaller cast of regulars (about five or six), and for them to be more than just their job descriptions. I'd also like to see a wide range of stories from dramatic, to non-stop action, to humorous, to even horrifying. It can still tell stories that offer food for thought, but also have stories about just blowing a lot of

up sometimes.
And while the series can still go about exploring strange new worlds, etc., it also can show life within the Federation and Starfleet too. I'd also be the series where the main characters--including the captain--can be written or killed off if the story demands it.