Bills (and resolutions) are the usual form in which legislation is proposed. More than 85% of bills introduced are never passed; they "die in committee."
Bills prior to 1989 (101st Congress) that were never passed can be difficult to locate. Bills are often reprinted in hearings; Senate bills are sometimes printed in the Congressional Record. Bill summaries can be useful when the text of the bill cannot be found.
See the Research Guide: U.S. Government Legal Information (Statutory Law) for information about bills that have been signed into law.
Private Bills & Laws:
Public laws are codified by subject in the U.S. Code
Private laws are not codified. Statutes at large in the only publication they are in.