Most of the early settlers at Jamestown died or gave up and went back to England, but a few settled and eventually found time for recreation. A fiddler came to Jamestown in 1618 and in that year, Governor Argall found it necessary to ban Sabbath-day dancing, fiddling, and card playing. In 1620, another musician named John Utie settled on the York River and that year Guy Fawke's Day was celebrated with "musicke and dancing." Music was part of life in early Virginia--we just do not know what music. Our best guess is that the musicians, whether amateur or professional, most likely played the tunes currently popular in their homeland.
For dancing tunes, the music in the Fitzwilliam Virginial Book (ca. 1609-1616) and Byrd's My Lady Neville's Book (1591) is a little too fancy for pioneers, but the tunes would have been played in their plain versions. Jamestown settlers would have known the music associated with Shakespeare's plays or mentioned in other theater works. Sometimes these titles can be found in early editions of The Dancing Master, 1651-1728: An Illustrated Compendium. Such would include tunes like "Hearts Ease," "Row well ye Mariners," "Joan Sanderson or the Cushion Dance," "Put on your smock a Monday," and "Sellenger's Round." Many of these can also be found in William Chappell's The Ballad Literature and Popular Music of the Olden Time (New York: Dover Publications, 1965).
When using The Dancing Master as a source, remember that the first edition appeared in 1651, two generations after the first settlers came to Jamestown. It is not necessarily an authentic resource for 1607. Tunes may have changed in the meantime.
For instructions on English country dancing, see The Playford Ball by Keller and Shimer (1990). This book describes early social dance in England and it includes dance instructions, music, lyrics for some early songs, and a good bibliography. For instructions on earlier dances, see A Lively Shape of Dauncing: Dancing of Shakespeare's Time (Wiltshire: Dolmetsch Historical Dance Society, 1994).
Chappell's Ballad Literature is the fastest way to locate song tunes and lyrics, although his music is presented in romantic 19th-century piano arrangements. For songs in period arrangements, a good place to find popular songs with their tunes is in books like Thomas Ravenscroft's Pammelia (1609), Deuteromelia (1609), and Melismata (1611). A facsimile reprint of these books was published in 1961 by the American Folklore Society. Here you will find such classics as "Three blinde Mice," "The Frogge would a woing ride," and "All in a misty morning" in their 17th-century versions. Some of these are multi-part rounds that are easy to learn and fun to sing. Ravenscroft's music has been published in modern editions as well. Look in books of rounds for pieces by Ravenscroft and other early composers.
For period ballads, go to Claude M. Simpson's The British Broadside Ballad and Its Music (New Brunswick: Rutgers University Press, 1966). Here you will find 540 ballad citations with their tunes. The lyrics are not there but Simpson tells you where to find them and when they were printed. Of the source he cites, the Pepys Ballad collection has been published in facsimile by Garland Press in a five-volume set. Hyder Rollins published a collection of Old English Ballads, 1553-1625 (1920) and the Roxburghe Society has published several multi-volume editions of early ballads. Check the dates carefully. Broadside ballads were printed in virtually the same form well into the 1800s.
Another way to find ballads is online. If you have the first line or title from Shakespeare or Claude Simpson's book, try searching for it. Someone may have put up the text. The Bodleian Library has put up images of a huge collection of broadside ballads, many of which are very old although the broadsides themselves mostly date from the 19th-century. Check their site at www.bodley.ox.ac.uk/ballads/.