Roughly from Constantine to the end of the Heraclian Dynasty.
I'm not a fan of 12 Byzantine Rulers, since in my opinion that podcast only repeats long outdated ideas about there being a European 'Dark Age', that Byzantium was the lone light of European civilisation and emphasises far too much the role of 'Great Men'. The concept of the podcast is fine, since it is perfectly acceptable to evaluate the reigns of 12 important emperors, but why did Brownworth have to resort to Gibbon to tell his story? History can't be reduced to protagonists and antagonists and I feel that some of his words are borderline hero-worship rather than an attempt at creating an introductory narrative to get people interested in this period. For a better introduction, I think The History of Byzantium podcast is much better, since the podcaster made an effort to read recent books on Byzantine history and are aware of how difficult it is to interpret the sources. It only begins in the mid-fifth century though, so it might be worth listening to the last fifty-or-so episodes of The History of Rome podcast; again, it's not super up-to-date and I'm not convinced that it offers a particularly nuanced view of history, but it is at least less polemical than 12 Byzantine Rulers.
All these podcasts however are overshadowed by recent and up-to-date books from some of the best academics who work in their respective fields. These are not unreadable ponderous academic tomes, but genuinely good reads from people who are doing their best to get the public interested in their work. For starters, you can't go wrong with Peter Brown's The World of Late Antiquity (1971), which is simply a classic and an excellent overview from the man who literally created the field of Late Antiquity. More up-to-date general narratives can be found in Chris Wickham's The Inheritance of Rome: Illuminating the Dark Ages 400-1000 (2009) and Peter Sarris' Empires of Faith The Fall of Rome to the Rise of Islam, 500-700 (2011). For something on Byzantium in particular, Judith Herrin's Byzantium: The Surprising Life of a Medieval Empire (2008) and Averil Cameron's The Byzantines (2009) are my standard recommendations. Robert Hoyland's In God's Path: The Arab Conquests and the Creation of an Islamic Empire (2014) is I think also necessary here, since he synthesises some of the most cutting edge research on the seventh century in his book, stuff that I doubt you will find in any other popular history book or in a podcast, so if you want to understand how the Arab conquests happened, pick this book over any other.