I would like to suggest that any competitors for the vital and prestigious role of Ship's Cook must of course settle the matter through a trial of arms (knives as befitting of this illustrious profession).

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Some potential roles (I can make random lists!):

First Officer: doesn't necessarily need the title/rank, but the Captain's right hand man/woman/thing
Engineer: fixes stuff, keeps stuff working, there could be a chief and assistant engineer (one more experienced/older, the other more of an "in-training" person)
Navigator: navigates, hopefully accurately
Quartermaster: keeps the supplies in order, 
Merchant: sells/buys the swag, knows their way around the Blackmarket
Helmsman/Pilot: steers the ship, ideally while sober
Armsman (Master-at-Arms): responsible for security on the ship and the [s]suicidal[/s] illustrious boarding party
Ordnance Master: in charge of ship weapons and ammunition (keeps peeps fighting), sort of like a more weapon oriented engineer
Ship's Surgeon/Doctor: fixes people, dispenses Vitamin C as needed
Master of Communications: deals with communications, master of duck-tape
Spy/Agent: someone who can figure out what is going on, has connections, knows some bad people and how to stop those bad people from murdering the ship
Boarding Party: captures swag, shoots fools, sing pirate shanties, short life-span
Ship's Steward: most important person on the ship, feeds the crew with hopefully delicious food
Researcher: could be an sort of archaeologist looking for alien artifacts, some sort of xenobiologist, or really any sort of scientist, researchers stuff (obviously)