Of all the ideas presented in this subforum, the one I find most interesting would be a focus on a group of junior officers serving together--perhaps a core group of three or four with some supporting characters as well.
For continuity's sake (in terms of paradigms anyway) I'd stick them on board Enterprise-G
, a huge vessel with a crew of roughly two thousand. We'd see the Captain or senior staff only once in awhile, and over time they might change--first officer moving up to command after the Captain gets promoted, etc. The main characters themselves would increasingly be seen as an effective team and thus assigned together for away teams and the like. During the course of the show this group might even get transferred to a new ship.
Me, I'd also avoid any clear sign whether this was the 'prime' timeline or not. You can certainly have Vulcans, but never mention that time Vulcan was destroyed back in the 23rd century. For example.