Fire barrels do very little against you, in most cases, so try to keep the rear of your primary target at your side, that way you can either ignore or destroy the fire barrels, continuously fire your cannons at them, and avoid their cannon fire completely, unless they get away from you. Basically, you'll be sailing in circles while they try to get you off of their ass. Practice just sailing, for a while, because you're going to have to get used to frequently switching sails. If you need to make a really sharp turn, quickly cut your sails, make the turn, then switch back to mid-sails. If necessary, switch to full sail to make up for lost ground water.
Oh, and once you have the level 2 or 3 ram, don't even bother shooting the small ships, unless they're behind you. Just ram them, and they drop.