There are several prominent series of publications from the U.S. Congress, including those from committees and from subsidiary sites. This list of Types of Legislative Documents, created by the Law Librarians of Washington, D.C., might help to clarify.
A few commercial publishers have digitized large quantities of Congressional publications. Searching and access often are easier than with free sources, but access is available only to current members of the W&L community.
These collections of Congressional documents are provided without-charge for all users by the Federal Government.
Online coverage generally begins with the early- to mid-1990's.
By far, the most complete resource for finding "historical" (old) Congressional materials is W&L subscription to ProQuest Congressional, listed above.
Before 1873, records of Congressional proceedings were kept under various titles -- Annals of Congress, Register of Debates, and Congressional Globe -- all of which are accessible in the Library of Congress's Century of Lawmaking site.
Here is an excellent overview of the historical development of the Congressional Record and related series, along with an outline of the component parts of the CR. Printed copies may be found in Leyburn Library's U.S. Government Depository collection.
Official and free.