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Dear Mr. Little,
The National Archives has a listing of resources at that you should try, if you haven’t already, at https://www.archives.gov/research/genealogy. U.S. Federal records will be helpful depending on when/where your family came to the U.S.
Another listing that would be of particular interest for you is one for the British Isles (including Ireland) at https://www.archives.gov/research/alic/reference/ethnic-heritage.html#british. These resources will be helpful for information about your family before they came to the U.S.
We hope this is helpful. Best of luck with your family research.