Your Captain is a Character like every other on board, but with much less managment needs.
He lacks visible food and energy bars, so presumably he has no need for those.
While (s)he also lacks a visible happyness bar, there still appears to be an effect on traits gain and there is a value shown on several tooltips.

You can normaly pick Specialisations for your Captain, but due to his importance it should be something that is more usefull while staying on the ship then during away missions and boarding parties.

All Characters (including the captain) have slots for 4 Traits.
Newly hired recruits often come with one trait pre selected.
Traits directly affect usefullness for certan specialisations or roles and thier gain is tied to happyness.

Perks are positive traits
Quirks are negative traits

Traits are seemingly gained over time in your service without any other influence (yet).
If a character gains a Perk or Quirk depends on the happyness of the crewmember when the trait is gained. In turn when the trait is gained the happyness shifts towards neutral to make certain there is still work needed for the next perk/room for the next one to be a quirk.
Perks also appear to be used to pick semi-random dialog lines ("My blood is so energetic, you could run the entire ship with it") for the character.

Traits usually come in clear pairs that affect one bar or one characteristic:
Depressed/Energetic: Affects need for sleep.
Lost/Pathfinder: Affects effectiveness while manning the nav computer.
Anti-Social/Social: Happyness gain from conversations

However quirks also appear to include special ones without proper positive perk to counter them:
Irritatable Bowel: Has to use toilet regulary. Happyness loss if none around.
Haemophiliac: Can't stand the sight of blood.

Whiteshirts:
When you get most characters (even your captain) they are mere whiteshirts. They have not yet picked one of the big paths

The best way to remidy that is to throw them into danger (boarding parties, anything mission related), and see who survives to gain enough XP for the Promotion. If thy also have 1-2 usefull (or hindering) traits under thier belt by then it will be so much easier to pick thier specialsation.
Of course the captain is the one big exception to that.

Why are they wearing white? So you can instantly see the blood when they die a horrifying death in hostile territory and know you can save the power on thier beamout of course!

Tactical (redshirt):
Oddly enough they are not truly like thier namesakes[tvtropes.org] - that job is already covered by SCG's whiteshirts.
They lead boarding parties, protect away missions from hostile (so most) aliens, counter enemy boarders and do other stuff that include shooting first, never asking questions.
They get access to specialised weaponry far beyond the normal handgun issued to all SCG personell.

Engineering (yellow shirt):
The engineers have it hard. Nobody thanks them for thier hard work, but often they are all that keeps your ship from becomming expanding clouds of space debris. Indeed they might be even more usefull then Ducktape, because who would apply it without them?
Thier basic ability is to repair stuff with scrap metal. Of course thier knowledge of ship systems might be used offensively too....

Medical (blue shirt):
They are like engineers for living things, just with more respect. They can keep your security healthy in the middle of a firefight.
The higher planned specialsatins imply some other use - like maybe removing quirks or engaging in diplomacy.

Unlike thier glorious captain, all those whiteshirts and rgb shirts have needs. Those are:

Food:
The bigger the crew, the bigger the amount of food they can consume and the longer the line at the kitchen. Be carefull that your army of shirts is not eating every credit off your account.

Energy:
Not only do they want food, they also want a place to rest. What a lazy lot!
Beds are best of course, but a simple seat can also work in a pinch.

Happyness:
While currently not nessesary, having high happyness means positive traits are gained rather then negative ones.