Just a note about surnames. Just because folks have the same surname DOES NOT mean they have ever been related to you. Surnames are a fairly recent invention and many derive from professions (Miller, Smith) location (Hill, Brooks) appearance (Large, Brown) or patrimony - son of (Johnson, Nelson). A few names are unusual enough, and have only one early immigrant, that nearly all people with that surname are related, but these are not common.
A good example is the name Hopkins. There were 5 Hopkins families who came to America in the early 1600s. They are not related. From Wikipedia: Hopkins is an English, Welsh and Irish patronymic surname. The English and Welsh derivations mean "son of Hob". It derives from the Germanic warrior name Hrod-berht, translated as "renowned-fame". It was 'borrowed' into French, where the spelling was changed from "Hob" to "Robert".
If you have Colonial Hopkins ancestors, you can undoubtedly trace back to one of these families, but not all. It gives you a one in five chance of being related to the Mayflower Hopkins.