I've written already quite a lot on the Burnham brothers, two of whom are my ancestors (Robert and Thomas). I've discussed how they were not on the ship Angel Gabriel. It then resulted in a discussion of when they did arrive in New England. So you can review those postings which remain up to date in their content.
1. Thomas Burnham born ca. 1618 (he consistently deposed his age for 1618 or 1619 in five depositions) and died at Ipswich, Massachusetts 19 May 1694. He married say 1643 at Ipswich, Mary Lawrence, baptized 10 April 1625 at St. Alban's, England and died at Ipswich 27 March 1715, daughter of Thomas and Joan (Antrobus) Lawrence. Mary arrived in New England in 1635 on the ship Planter with her mother and siblings. Thomas's will at Essex County Probate 304:436, #4174. They had twelve children: Thomas, John, James, Mary, Johanna, Abigail, Ruth, Ruth, Joseph, Nathaniel, Sarah and Esther.
2. Thomas Burnham born Ipswich about 1644 (based on five depositions) and died there on 21 February 1728. Thomas married first at Ipswich on 13 February 1665/6, Lydia Pengry, born about 1645 and died at Ipswich 14 March 1689, daughter of Moses and Lydia (Clements) Pengry. Together they had eight children: Thomas, Moses, Lydia, Aaron, Eleazer, Abigail, Daniel and Mary. Thomas married secondly at Ipswich on 16 December 1689, Hester Cogswell, widow of Samuel Bishop. She was alive in 1704, but likely dead before 4 October 1711 when her sons Samuel and John Bishop deed land without her.
3. Mary Burnham born Ipswich 18 October 1685, died Norwich, Connecticut after 11 October 1748. She married at Ipswich 23 December 1710, Samuel Story, born Ipswich 10 January 1683/4, died Norwich, Connecticut before 2 September 1747, son of Samuel and Elizabeth (---) Story. His will in New London Probate #5193. Ten children: Samuel, Mary, Joseph, Ezekiel, Jonathan, Lucy, Abigail, Elizabeth, Lois, and Jabez.
Sources: Mary Walton Ferris, Dawes-Gates Ancestral Lines vol. 1 (1943) and vol. 2 (1931).
The Great Migration Immigrants to New England 1634-5 by Robert Charles Anderson, (Boston, MA, NEHGS, 2005) Volume IV:258-259.
“A Doleful Slaughter Near Black Point: The Battle of Moore’s Brook, Scarborough, Maine, June 29, 1677” by Sumner Hunnewell, Maine Genealogist Vol. 25 (2003):51-72, 99-120.
Boston Evening Transcript, 12 Dec 1927 (#6418).
Pratt, Robert L. The Descendants of William Story Who Came to Ipswich, Massachusetts in 1637, The First Eight Generations (Gateway Press, Baltimore, 2000).