17th century England. King James VI of England is dead; his son Charles has gained the Crown. Pirates from Barbary prowl the high seas. The British Empire continues to expand. You are explorers and sailors aboard the HBMS Visage, one of three ships (the others being the HBMS Valiant and the HBMS Victory) sent to establish a colony in Barbados.
That was then. Years ago. Your ship wrecked on an unknown island after a colossal storm sent you way off course.
There were hundreds of you. Slaves, sailors, soldiers, explorers, and volunteers. Many tons of cargo went with you--food, clothing, equipment, weapons (including gunpowder weapons), maps, books, and building materials. All of that is spread out around this God-forsaken island, fought over by the various factions that have arisen.
What's the state of the failed colony now? What is the nature of the island you're on? How much of the original population has survived? Has it been long enough for a second generation? Are there natives, and if so, what is their nature?
Inspired by this post
by John Harper on The Mighty Atom. Historical fact checking very welcome. I'll post some mechanical ideas some other time.
 His Britannic Majesty's Ship, later replaced by HMS.