The oldest existing school of Buddhism comes in the form of the Theravadin Orders of monks and nuns.
In Buddhist Books Podcast, a distinction is made between "Pre-Sectarian Early Buddhism" and "Theravada Buddhism." The reason for this is that modern Theravadin Orders more closely resemble the Sanghas which existed after King Ashoka sponsored the Third Great Coucil of Buddhism approximately three centuries after the time of the original Sangha. These orders developed over time, and were also informed by the several great Buddhist Scholar-Monks who wrote commentaries on the Tipitaka after Mahayana had become popular, a millenium after the time of Lord Buddha.
The Tipitaka is, indeed, the most important part of Theravada Buddhism, and the monks and nuns of modern Theravadin orders live mostly according to its rules and teachings. In the future, Edward will read aloud the commentaries of Buddhaghosa and others, and they will be linked to on this page.
For now, if you would like to hear the recitals of the Tipitaka, please click here: