Having learned how to PvP eons ago, I'm still not sure whether I know everything that's the common protocol these days - but, I think I've got it down.
First, as soon as you enter a match, try and work out a rule system. Keep it short - "Blades only?" means a match for only swords and daggers, "Anything goes?" means.. well, anything goes, "No jumping" means none of that crazy jumping business, etc. Of course, if your opponent chooses to ignore the rules, feel free to assume they are abandoned and go ballistic. (Unless you're the "honorable type" and stick with the rules anyway - but, who really believes in an honorable pirate?
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My weapon of choice, as others have suggested, is the broadsword, which I usually use regardless of the match type (except, of course, when the match calls for their banishment, to which I sob to heavily.) They're very good for being able to move around your opponent, yet still manage to hit them.
It's also good to keep in your belt some throwing knives, and good gun (pistol or repeater, and maybe a musket or bayonet - blunderbusses are a hit or die situation.) But, other than that, the only thing I really can suggest is learn to move around your enemy.
You don't necessarily have to jump, but learn how to move around while fighting. I'm positive I'm not the only one who can around here - there are plenty of pirates with all types of fighting styles out there. Try and see if you can get them to help you out, because strategy above all is key in PvP.