Some stuff from films, books and games that would add some flavor:
Heated shot from shore batteries. Fire ships. Ships on fire.
Wardroom issues. What if the brilliant tactician you signed on as First Officer is a tyrant that lowers the morale of the whole crew? What about the Lord's nephew who is a worthless poltroon?
Prize money.
Marines.
Admiralty orders...sometimes not the ones you want.
The pain of seeing the crew you've picked and trained killed or maimed in battle, and dealing with the raw replacements you get.
Individual heroism...maybe tied to the above. Do you chance losing a skilled officer by using him for a "boost" in an important action?
Do your actions in regard to prizes, discipline and battle effect your ability to recruit crew? Your relations with other captains?