Before the Presidential Records Act of 1978, all presidential papers were considered the personal property of the president, and presidents took their papers with them when they left office. The Presidential Records Act of 1978 designated any document produced during the course of the president's official duties (by both the president and his or her staff) as official, public records, and as such those documents become the property of the nation. Since 1981 each departing president has been required to deposit any such records with the National Archives and Records Administration.
The Presidential Records Act obviously does not apply to nineteenth century American presidents. The papers of nineteenth century American presidents exist in varying states of completeness, and some no longer exist at all. Many were subsequently acquired by the Library of Congress, and they have made the papers of several nineteenth century presidents available online. Some are still only available on microfilm.
Bear in mind that these "presidential papers" will include a mixture of personal and official papers.
The Library has a large collection of digital collections. Above we list several that would be especially relevant for this class, but for many more digital collections, consult: