A Frigate, with Cotton Sails and various other upgrades.
Usually, I start my career capturing ships and selling them for a profit. This is risky, though, because you're always sailing around in either a captured Spanish Merchant Galleon or similar, which has low Rigging and can't escape things you can't afford to surrender to, or in a fairly cheap ship like a Coastal Barque or Barque or (at a pinch) Sloop that you traded in your captured ship, and the cheaper it was the more money you got for the trade-in.
After I've been going for a while, though, and I decide I've saved enough, I start looking out for a Frigate. I might upgrade via a Brig or a Brigantine, but ideally I jump straight from whatever random ship I last seized up to the Frigate.