Gad Heuman's The Caribbean: A Brief History is a very good place to start if you're interested in the history of the Caribbean region in general; it's a highly accessible collection that takes in a range of topics. It's not a terribly long or detailed read, but Heuman is a thoroughly impressive historian who does a stellar job at taking you on a whistle stop tour of the region. Nicola Foote's The Caribbean History Reader is a similarly impressive collection of essays that taken together make for a good survey course of Caribbean history, although much of that collection deals with history well after the time period that you're interested in. Richard Dunn's Sugar and Slaves: The Rise of the Planter Class in the English West Indies, 1624 - 1713 is another volume that's enormously useful that you should be able to get your hands on fairly cheaply - it's a little old now but still a very useful introduction to the 17th century British Caribbean. It's perhaps also worth checking out The Atlantic World: A History, 1400 - 1888; this is a substantial volume that deals with many different aspects of Atlantic history and can provide some useful contextualisation. Although it's a little after the period you're interested in, Trevor Burnard's Mastery, Tyranny, and Desire: Thomas Thistlewood and His Slaves in the Anglo-Jamaican World is one of the best books available for understanding what life was like for the white elite in the British Caribbean during the 18th century, whilst his recent book Planters, Merchants, and Slaves: Plantation Societies in British America 1650 - 1820 is a very compelling examination of the socio-economic development of British slave societies in the region.

Not an expert on the historiography of pirates, but Colin Woodward’s book, The Republic of Pirates, was a good read. It’s been a while since I read this, but I remember being engaged by it.