Privateer--Hoplite Unless you want to take the lead with the Sentinel, or be the missile master with the Harbinger, most will probably find the ship that does the boarding is the place of action, fame and fortune. Later when stealthy ships are available, the Prowler and Eclipse will replace the speed team, but to start choose wisely. Choose Vanguard.
Salvage--Reclaimer Is there any other?
Exploration--Carrack It is too beautiful a ship to not have in your collection, and the bridge is too pretty to go without. Alternatively, it is possible a StarG with a dozen Reliant Sen's will actually do a better job. If you can program the NPCs to fly and refuel constantly, this makes for interesting gameplay. No doubt though, you still have to own a Carrack. There is a rite of passage involved. Without a Carrack you are not an explorer!
Espionage--Tarrapin Sneak! Possibly the best Polaris scout or "ship's boat", since it can track active and passive to greater range than ships like the Hornet Tracker, and yet is going to be insanely hard to find. If Chris Roberts' dream comes true and we can link radar and communications ship to ship, using the Terrapin to scan for the Polaris could be a shockingly effective combo, with size 10 torps seemingly appearing from nowhere.
Smuggling--Mustang Omega Yup. Even the Xian Scout and the Herald cannot catch it, and it fits 10 standard cargo units. All of the Mustangs make the best smuggling ships in the 'verse, and there are so many of them, how could anyone catch you? Why would they think to?
Bombing--Eclipse Ya think?
Combat--Polaris If you want to rule on the battlefield, you want a Polaris. People often note that this is going to be an expensive ship to fly, but remember that the mission rewards are sized to the needs to complete them. Just running missions for the son's of Orion against Vanduul targets, you could earn a hefty living and have the UEE pay for all those missiles on each mission. There ARE ways to earn a living as a mercenary. You just have to be willing to kill things and take their treasure.
Command and control--Polaris Ditto. Idris is too big to be easy to crew, and will be too slow for a Command ship.
Solo play--Sentinel Just 'cause EM Warfare is so much fun. If you don't mind your prey hating you for messing with their heads, fly this bird.