This era (and region) wasn't my specialty. But it would appear that the Pilgrims (aka Pilgrim Fathers in the UK) were Congregationalists as seen with the Congregationalism they set up in New England. My understanding is that significant Presbyterian immigration came later and tended to be to Mid-Atlantic states like Pennsylvania, with many Scots-Irish of a Presbyterian background ending up in the South one way or another. Baptists in the USA (with regard to attaining much prominence) appear to have arisen with the First Great Awakening. Whitefield said something like "all my chickens have become ducks!"
See also the differences between the Congregationalists/Independents and the Presbyterians in the Wars of the Three Kingdoms, including the English Civil War.