I must say that I've actually put a lot of thought into this... My ship, a simple Caravel, would be named the Arsenic Dagger.
(Caravels were about 80 feet long, and mainly used by Spanish and Portuguese traders, though I find them to be useful as pirate's vessels, as well.)
It would fly only with sails of a sapphyre persuasion, thus blending well with the sea behind them. The flag, I would have to have a skull with bat wings protruding from it, the lower jaw removed, and a dagger placed vertically through the skull at a perfect 90 degree angle, displaying in bold crimson the blood dripping from the unfortunate skull. The eye sockets bleed, though there is no visible reason.
Freshly stocked drink... This one got me at first, as I was strongly considering rum. Although I then recalled that rum tends to make me a rather vulgar individual, and, even as a pirate, I would prefer to remain somewhat charming, thus adding to the mystique of my crew. And so I think I would keep it increasingly well-stocked with a variety of red and white wines. Of course, the crew would not enjoy this, and so I would allow them to partake of smaller amounts of rum, so long s no one at port finds them offensive. Even as a pirate, there's no excuse for discourtesy.