See "A Line of Descent from Thomas Stafford of Warwick" in the RI Genealogical Register, Vol. 17, by A. G. Beaman. According to Beaman, Thomas came to Plymouth Colony about 1626, then to Providence, and soon afterward to Warwick where he lived the rest of his life.
Note copied by Trish Harmon, posted on RIKENT mailing list: "Thomas, father of Samuel, was in Plymouth, Massachusetts as early as 1626, of Portsmouth and Newport, Rhode Island in 1638, then of Providence, Rhode Island where he constructed the first grist mill at the mouth of the Moosausick River; he moved to Old Warwick from Providence in 1650 and at the head of Mill Cove built a grist mill for the settlers. Was admitted freeman in 1638 (source: Stukely Westcott book by J. Bullock)."