Right. No ideas save one and it's a REALLY dorky one: My Star Trek Dream Crew!
Captain- Jean-Luc Picard (The Next Generation)
First Officer- T'Pol (Enterprise. Yes, I'll often pick hot chicks just because)
Chief Engineer- Montgomery 'Scotty' Scott (The Original Series)
Chief Medical Officer- Leonard 'Bones' McCoy (TOS)
Nurse- Alyssa Ogawa (TNG)
Chief of Security- Tuvok (Voyager. Because black Vulcans are badass)
Science Officer- Spock (TOS)
Random Civilians on board (every show has them)- Nog, Quark and Rom (Deep Space Nine), Kes (Voyager)
Counselor- Deanna Troi (TNG)
Navigator- Hikaru Sulu (TOS)
Communications Officer- It's a toss up between Uhura and Hoshi Sato but I'll go with Hoshi (Enterprise)
Operations Officer- Worf (TNG and DS9)