The basics: The Scots-Irish DNA project recommends the 111 marker Y chromosome DNA test. If this is not within your budget, the 67 will do and the 37 is an acceptable start. We use the Family Tree DNA lab in Houston, Texas.
Who are the 'Scots-Irish?' Or Scotch-Irish? Generally speaking the Scots-Irish are the descendants of settlers to Colonial and early Republic America from the nine counties of the province of Ulster, in Ireland. As a group the Scots-Irish were majority Presbyterian, though not all were and most descended from Scots families that had migrated to Ireland. Also of note, some 'Scots-Irish' migrated to the Colonies from other parts of Ireland outside of Ulster.
The main migration of Scots to Ireland came during the Ulster Plantation (circa 1609 to early 1700s). These Scots came primarily from the Scottish Lowlands. There is also a substantial number of Highland Scots that became Scots-Irish. Most of these Highland Scots descend from families from Argyll, Lennox, and the Hebrides, that migrated to Ulster in the 1500s.
There are other components of the Scots-Irish which include French Huguenot, Manx, and Border English, who settled in Ulster and migrated to the New World in the Ulster Migration. They married into and became part of the people and society we now call Scots-Irish.
There was also a large migration of Presbyterian Irish into Canada in the nineteenth century. They went mainly to New Brunswick and Ontario. Many of these families were of 'Ulster Scots' ancestry from both Lowland Scottish and Highland Scottish ancestry. In the past the term Scots-Irish has not been applied to this group, but increasingly the term has expanded to include the descendants of the Canadian migration. Nomenclature has been problematic in regards to the Scots-Irish for a long time. The term today reflects a better awareness of the descendants of Ulster Scots in the Diaspora.
Most families 'know' or self-identify as Scots-Irish. These are the families that are participating in the Scots-Irish DNA project.