Keep track of your research on a spreadsheet if you are searching for specific public records. Take notes, keep a record of where you've searched and whether what you've found is free. Records, both free and for a fee, will be found at the same source.
Start your federal records search by checking out the U.S.A. Government search engine, usa.gov. Hundreds of types of services and documents can be found there and most are free. You can even ask a government librarian to help you.
Search historical, economic, FCC, congressional and National Security Archive documents that are on usa.gov. The National Archives and Records Administration, archives.gov, preserves documents and ensures public access to the records.
Begin your incarceration records search with the Federal Bureau of Prisons' Inmate Locator and Facility Locator, bop.gov. These are federal, not state, records but a good place to start. Some states have systems that offer searchable court databases to the public. You have to search each state's website to find free records. Start with theinmatelocator.com.
Start your search for free genealogical information with the Church of Jesus Christ of Latter-day Saints at their genealogy site, familysearch.org. Most other genealogical sites will list names but require a fee for your access.