Well, the crew in the series was Malcolm Reynolds (ex soldier, now captain of the Serenity), Zoe (another soldier who served under Mal in the war, now first mate), Wash (sarcastic pilot and Zoe's husband), Jayne (a greedy merc who joined looking for a better deal), Kaylee (ship's mechanic, very cheerful). They pick up several passengers in the first episode, Book (preacher with a hidden past), Simon (doctor, a fugitive since he broke his sister out of some Alliance academy), and River (the sister, also a fugitive, who the academy experimented on.) And then there is Inara, the companion, who is sort of the ambassador, helping to make things look "respectful."
Maybe one of those characters might give you an idea? But, for a list:
Captain: someone in charge.
Hired guns/deckcrew: Muscle in case things go badly. As well as for loading and unloading cargo.
Mechanic: To fix the ship.
Pilot: Fly the ship.
Medic: To fix the crew when they get shot up. Its a dangerous 'verse after all.
JUst some ideas, if you want to play something else, let me know.