Having trouble finding an answer to this. I know that the oldest English translation of the Bible is the Tyndale Bible, written in the 1500's. What was commonly read in the late 1600's? Specifically in New England during that period.
The favored translation of the Puritans (and hence most English speaking inhabitants of New England) in that period would have been the Geneva Bible, which was first published around 1560. The Geneva Bible went through over 70 editions between 1560 and 1640. That version included annotations, which were somewhat controversial because some of them were seen as undermining royal authority.
After the Restoration in 1660, the King James Bible (which was first published in 1611) became increasingly popular. It would have begun to replace the Geneva Bible as the preferred English-language translation before the end of the century.
Sources:
Campbell, Gordon. Bible: The Story of the King James Version. New York: Oxford, 2010, 23–28.
Engen, Abram Van. Sympathetic Puritans: Calvinist Fellow Feeling in Early New England. Oxford University Press, 2015.