I think you'd be looking at gradually ramping up the serialization over time, whereas the first couple of seasons would be mostly stand-alone with some nods at the overall developing series arc. That way you don't immediately lock out new viewers by jumping into full on serialization. There's a lot of shows I would have liked to watch but I didn't hear about them until well under way and I didn't feel like catching up on the story, so no viewership from me. "24" and "Lost" are two of these, pretty well liked by most but I've never scene a single episode. Same with "Walking Dead".
I'd also say artistic freedom for the writers would also be high, no "A+B story" type rubbish rules, or "Must be on a ship with a [Insert Race/Gender] Captain". You are bound by what is known about the Star Trek universe, but apart from that, it's all fair game. If it's a post DS9 series, maybe we'll destroy the Federation, or have Earth occupied by the Romulans, or something like that. Humanity might be a remnant like Guinan's people, but in the end will endure. Think big. Maybe a sleeper ship sent to the Andromeda galaxy, waking up after 300 years in intergalactic space, only to find that...