Another good podcast on the subject is Lars Brownworth's 12 Byzantine Rulers (http://12byzantinerulers.com/), which starts with the Roman emperor Diocletian and proceeds through the founding of Constantinople, the fall of the western empire, and the evolution of the eastern empire over the 1,000 years that followed.
Mike Duncan has since moved on to Revolutions and is currently in the beginning of the French revolution. Don't let that slow you down, its not like the history of rome is going to change much in the near future.
Then "the history of rome" podcast begat "the history of byzantium" podcast. Another investment in time which isn't nearly done yet.
There is also the British History podcast which is pretty good listening and technically on topic as it was partially part of the roman empire for a good while. Another work in progress.
(And I see sspiff and I posted within seconds of each other. Well, great minds think alike and all that...)
He wrote a book on the eastern "Byzantine" empire as well, Lost to the West, which covers some of the same ground as the podcast series but plenty of other material as well.
Also by Lars -- Norman Centuries -- fascinating account of how Vikings ended up ruling Britain, Normandy, Sicily and leading crusades. http://normancenturies.com/
