The correct response is as follows.
These associations are accurate.
New Hampshire was a royal colony. The King of England appointed a governor to oversee governance.
New York became a proprietary colony, conferred to the Duke of York by King Charles II as a mark of loyalty.
Jamestown was classified as a corporate colony. Several affluent English individuals engaged in funding the voyage to the Americas aiming to colonize part of North America, managed by an English joint-stock company.
The very first English colony on American soil was Jamestown, Virginia, established in 1607. Following this, a group of Puritans found the Plymouth colony in New England in 1620, escaping persecution from the Church of England. During the Colonial period, the total number of colonies set up by English settlers amounted to 13.