I have two,lol. For invasions my favorite weapon to use is the Shadow Stalker Repeater Pistol, with Hex Ward and infinite silver shot. The attack is only 22 but is does well for invasions. Then my other favorite is sword, which would be Bitter End or EP's lost sword.
I prefer to use Darkfire for some reason even though I have a lot of weapons that do a lot more damage for some reason I just really like it. During invasions I tend to use a repeating pistol with infinite venom shot... its a really great one that usually takes most things out in a single shot including keg runners.
My first year on pirates, hands down, voodoo staff / wither was BY FAR my favorite, just for its pure awesomeness. (Damage point on it used to be a lot higher and it was the only weapon that could take out an enemy behind me.)
These days, my basic pirates live by their blunderbusses.
My unlimited pirates favor broadswords. But baneblast repeater (rank 5 venom, rank 7 bane) is the main tool for powder keg runners. When gypsies appear, it is viper's nest time. Grenades of course, get used a lot during invasions.
Oddly, I use doll more than anything (healing, cursing, curing, shackles and a life drain once in a blue moon.)
With F5 and F6 still broken, I really don't use staff for anything, now.
'Twould be nice to be a pirate again, living by the strength of me broadsides!
I voted for the sword of course, I like the combat styles, variety of sword types, and I also like how you seem to get more experience with it. My sword I use is a Dragoon's Broadsword that does 65 damage. I know it is not much, but it is better than the 15 damage from a basic weapon. The weapon I see the most from other pirates is the sword as well.
When I first started playing POTCO, for the first time, I was obsess with my Doll, and was so proud of it, and I would use nothing else much, but then I took a brake for 6 months, and when I came back I decided I was going to switch weapon, and from then on, I have not used dolls at all since then, and now days I don't eve get a doll, for example, on my pirates treasurer I got doll until I was like level 30, and on my other pirate level 26 I don't even have a doll.
I started using gun more, and when I had mastered gun, then I started using sword, and then dagger. But now days, I favor sword and dagger, they are not as easy to level as it is doll and gun, but I like them because they are a bit harder to level and makes it a bit more challenging, and in time you get used to it.