Port Royale 3 is an open-ended game, so players can choose to pursue any career they wish.
This could range from a business tycoon to a pirate. Initially, you must trade goods between Caribbean colonies to make money, but over the long term you can have substantial business interests in many Caribbean ports, and support large fighting fleets.
As a business tycoon, you trade with towns to gain their friendship, and can then buy building permits to establish businesses there. Ultimately, you can even come to have your own town, but this can take a very long time.
As a buccaneer (with a Letter of Marque), you can attack any of the four colonial nations in the Caribbean circa 1600; from largest to smallest: Spain, England, France, and Dutch. If you have not acquired a Letter of Marque, every nation will see you as an enemy - you are a pirate.