Which colony group did most Puritans move to?
The answer to this question is that the great majority of the Puritans who moved to the colonies in what is now the United States moved to the colonies in the area that we now call New England. The Puritans were the first European colonists to move to this area and they established colonies that attracted more Puritans to join them.
Americans, of course, know the story of how the Pilgrims came to Plymouth Rock in Massachusetts. The Pilgrims were one group of Puritans. The came to the Americas in an attempt to find a place where they could dominate the government. In England, the Church of England was the official religion and the Puritans wanted to have a place where they would be the official religion. After the Pilgrims came to Plymouth, they were joined by other Puritans who founded the Massachusetts Bay Colony. This attracted more Puritans to the region.
The short answer to your question, then, is that the Puritans moved to the colony group called New England.