You will probably want to search local (city, county, region or state) records for traces of your ancestors. The Library of Congress has copies of published transcripts, abstracts, and lists from many church and government records.
The best way to locate these resources is by searching the Library of Congress Online Catalog.
Alternatively, use the "Keyword" function to enter any words that describe the location or type of records that interest you. Click on any title to see a detailed bibliographic record and to request any items from the stacks. You may request books from the Library of Congress collections one or two days before your visit, or on the same day if you will be staying in the Library for research. Most retrievals take about an hour, although some take longer because the materials are stored offsite (which is noted in their catalog records). There is no limit to the number of books you can request, but plan for the time you have and how you want to spend it.
Here is a list of the kinds of records you might find at a county courthouse. Classification and collections differ between jurisdictions.
Here are a few tips for searching courthouse records.