I agree there needs to be a better mission system for PvE. While I like the game being more sim than arcade, good missions would probably bring in a keep more causal gamers.
Ideas I've had, with descriptions to add flavor-
Search and Destroy (what we already have)- Local merchants have reported pirates operating in the area. There appears to be one, possibly two vessels , most likely 7th or 6th rates. The local Navy commander orders you to proceed to their last known location and sink, burn, or take them a prize. (add the two vessel part if the mission will have two opponents so you know what you'll be getting into, the rating range to know how big an opponent)
Local Security Patrol- Fleet commanders desire more safety for our shipping in the area. Patrol between (port) and (port) and engage any warships sailing under the flag of (other faction). (missions would only pop in your factions areas where AI warships of other factions are spawning, and either a set number of kills or a time limit)
Foreign Security Patrol- Same as above, but in waters controlled by another faction. Would also have a warning about possibly meeting 'superior' enemy captains (other players).
Custom Inspection Patrol- Smugglers have been reported in the area. Patrol from (port) to (port), inspect any merchants you find for contraband. (same as patrols above, but against merchants (same faction or other), with the ability to order them to 'heave to for boarding'. Most will give a message 'no contraband found during search', while the smugglers will be flagged with the contraband tag and attempt to flee from you.)