TL;DR version because I'm hopped up on Nyquil
A captain should be charismatic, loyal, logical, and aware. Honestly, an Eve veteran would be good here, especially if they flew capital or squad command. They need to be able to both Macro and micro, but focus on the Macro. I personally believe there should be some form of test to this, like a google docs form, before someone who is not a capital ship owner can use a cap ship.
Crewmen. I'm splitting this into 4 groups.
Sub-commanders. These people are in charge of divisions such as guns (split based on ship design), engine room, shield, scanners, etc. they are to do the majority of the micro. They need the same qualifications in general as the captain, but able to lead and be lead.
Wing commanders: See above, but they are in charge of fighter squadrons.
Wingmen: Follows wing commanders. Quick thinking, self-sustaining, and thinks for the sake of the group as a whole.
Crew members: Able to manage themselves appropriately, take orders, and follow the rules of silence.
Rules of silence: Captain has full override. He can talk whenever he feels is appropriate to issue commands. Commanders: Silent at most times. Freedom to talk to members, but needs to pay close attention for captain commands. Crewmen: Only report if absolutely needed. Wingmen and Wing command: Split into separate comms if need be since there will be a lot of chatter for fighter wing op
Secret edit: This is for during-operation. In casual non-op people should still respect their superiors, but the comms silence rules don't apply unless alarm sounds.