I'm of the opinion that a Trek show should have a group of regulars, who generally appear in the majority of episodes, but also should have reoccurring characters that pop up when a story demands it. With those
supporting characters mixed in the regular characters, you can do quite a lot.
But I've said this before in many other threads like this one, that characters should be allowed to come and go when necessary, including the captain. But at least you can start off with an initial group of regulars and work from that.
For example, C.E.Evans gave a very brief list of the senior positions aboard a ship. I'd suggest giving each of his characters a name,
I intentionally didn't give any of my characters a name nor an ethnicity other than human or alien for brevity's sake (I'm not writing an actual fanfic here, just some basic character ideas--further details to be filled in later).