[MaddogK]

If you mouse over the crew you'll see a description of the specialties. My observation is the higher the numbers for a trait the better they perform at a given task. i.e. a crewmember with 100 elec and 50 mech will perform a repair faster on batteries than a crewmember with 100 mech and 50 elec.
The engine room crews seem to perform better with higher mech skills than elec skills.
The gunner shoots planes down faster/with less shells with high gunnery points (the gunnery specialty helps alot too).
The sensor specialty looks like a generic trait for the conn crew until you start to get specialists, so I replace the sensor crew with radar experts/sonar experts when they become available, and put the sensor guys (which have very high elec skills) into the DC shop or trade them off for torpedo guys.
I find the seamen with high mech skills do well in the torpedo rooms and engine rooms so I don't bother shopping for specialized petty officers to fill empty spots in these rooms if I have at least 2 torpedo PO's per room, per watch.
The command crew I haven't quite figured out yet but I keep at least 2 per watch, and trade the rest off for other petty officers I need. I suspect they make the boat maneuver faster.
You always want a specialized gunner (Chief petty officer or above- 120 or higher gunnery score) at the AA gun, and I prefer to m an the deck gun myself.
The higher watch score guys you want as lookouts as they can spot ships/planes further away the higher their score is.
...And finally you want the guys with the higher leadership scores running their area of the ship- makes their 'team' more efficient. I usually keep 1 officer per compartment (aft torpedo, engine room, conn, etc) but not necessarily all in the same watch as it is generally navy tradition.

Fatigue appears to effect efficiency when the numbers get too high, but I normally don't worry too much about it as the rotating watch schedule keeps the numbers low, and I DON'T normally call GQ whenever I see a ship- only when I'm being chased or in a heavy convoy area, and I always allow the crew 24 hours to rest before considering calling GQ again.

Your observations may differ, good luck.