I'm going to go with characters that I think would interact in interesting ways. Be it in single lines of dialog, or having the characters broken into pairs and having entire episodes revolve around them.
Setting: maybe a galaxy class star ship lost in the Delta quadrant. A bit of TNG and a bit of Voyager with some of DS9's moral "grayness".
Bridge crew characters:
Captain: Sisko
First Officer: Spock
Helm/Second Officer: William Riker. Half hot shot and half seasoned professional with an air of command. And a cool beard.
Tactical: Data. The ol' positronic brain would come in handy at this station, I think.
Ops: Nog.
Non Bridge Crew characters:
Chief Medical Officer: Bones
Chief Engineer: Oh man this is a tough one. Torres, Scotty and O'Brien are all great characters. I would watch a show just centered around the three of them. I'm gonna cheat a bit and make O'Brien the Chief, and have B'Elanna be his hot headed right hand man.
Science Officer: Seven.
Security: Odo
Recurring characters:
Counselor/Dispenser of Booze: Guinan
Young Vulcan Officer: I liked the dynamic between Spock and Saavik in the Trek films. I think T'pol would fit that role perfectly.
Ship's Ambassador: Elim Garak