My answer is mostly focused on North Carolina, specifically with Scottish Highlanders, but they had to pay their way in essentially. Ones that could afford to buy the land grants would usually bring their entire families and clan to the area. Around the 1740s most Highlanders were able to afford the journey from Glasgow to North Carolina, and buy in on the land grants that were available at the time. About £10 was needed at the time but that did not include tools, housing, or land. Only a minority needed financial assistance for the passage across, which meant either indentured servitude or finding donations. Catholic Highlanders found donations through the church and various charities.

There was also an incentive when in the 1730s Governor Gabriel Johnston gave tax exemptions for immigrants for ten years if they were "foreign protestants." This was extremely helpful for these families. It's akin to buying a car today that is medium priced with a small down payment and then having no external fees for 10 years. This example does however require the assistance of a benevolent governor who will outright support incoming immigrants. There is a passage in the records where the Upper Assembly questioned him on allowing so many of his kinsmen in, especially when a number of them were former "rebel Jacobites." If one was able to buy land or find servitude until could own the land then one was able to settle. An Ellis Island or the like did not exist in this time. All one needed to do was swear allegiance to the crown after getting off the boat, which could be done at any court. I've only read of very instances in the records where a certain amount of years as a resident was needed. Most of the time it was swearing an oath, payment of two schillings, and finding land.

Bibliography:

Colonial Records of North Carolina

Duane Meyer, Highland Scots in North Carolina

Arthur Roger Ekrich, Poor Carolina: Politics and Society in Colonial North Carolina, 1729-1776