Reddit mentions of Justinian's Flea: The First Great Plague and the End of the Roman Empire

All credit to Robin Pierson at the History of Byzantium podcast. Truly fantastic work, careful though it's easy to get sucked in.

Justin takes power-
http://thehistoryofbyzantium.com/2012/11/

The best book might be Justinian's Flea by William Rosen though it concentrates mainly on Justinian obviously.
http://www.amazon.com/Justinians-Flea-First-Plague-Empire/dp/014311381X

The standard textbook history right now appears to be The Romans: From Village to Empire.

Klaus Bringmann's A History of the Roman Republic also still seems to be the standard introduction to that period (i.e. the time period of Imperator).

If you want to read about the end of the Roman Republic and Caesar/Augustus, it's hard to turn down Caesar: Life of a Colossus which is great for the general reader, alongside his Augustus: First Emperor of Rome.

He also writes pretty solid books on other major Roman figures, such as In the Name of Rome: The Men who won the Roman Empire.

If you want to get a pretty good introduction to Roman History, but more of what life was like for the average citizen, SPQR by Mary Beard is actually a good choice.

Older, but still solid, is Peter Garnsey's The Roman Empire: Economy, Society, and Culture which covers a lot of things Beard doesn't.

For the Roman army, Adrian Goldsworthy's The Complete Roman Army is a solid introduction.

However you'll want to break that down into several books if you want to go deeper:

Roman Military Equipment by MC Bishop and JCN Coulston

The Roman Imperial Army of the First and Second Centuries AD by Graham Webster

A Companion to the Roman Army by Paul Erdkamp

For the collapse of the Western Roman Empire I'd recommend both Peter Heather's The Fall of the Roman Empire: A New History of Rome and the Barbarians combined with the more scholarly Guy Halsall's Barbarian Migrations and the Roman West.

For the forgotten half of Roman History, often mistakenly called the "Byzantine Empire," it's hard to cover with just one book, but Warren Treadgold's A History of the Byzantine State and Society has become the standard reading. John Haldon's The Empire that would not Die covers the critical transition during the Islamic conquests thoroughly.

Of course I have to include books on the two IMO most overrated battles in Roman history on this list since that's what people love:

The Battle of the Teutoberg Wald: Rome's Greatest Defeat by Adrian Murdoch

The Battle of Cannae: Cannae: Hannibal's Greatest Victory is sort of the single book to read if you can only pick one. However, The Ghosts of Cannae is also good. But if you actually want to go really in depth, you need Gregory Daly's dry-as-the-Atacama book Cannae: The Experience of Battle in the Second Punic War. When I say dry as the Atacama, I mean it, but it's also extraordinarily detailed.

I'd complement this with Goldsworthy's The Punic Wars.

For other interesting topics:

The Emergence of the Bubonic Plague: Justinian's Flea and Plague and the End of Antiquity.

Hadrian's Wall: Hadrian's Wall by Adrian Goldsworthy

Roman Architecture: Roman Architecture by Frank Sear (definitely a bit more scholarly but you can probably handle it)

I may post more in addendum to this list with further comments but I think I'm reaching the character count.

Related:

> Justinian’s favorite hobby, in fact, was arguing the most obscure points of Christian doctrine (you can easily see where we get the dictionary definition of “Byzantine”). This was brought home to me by way of one really illuminating scene that I included in the book; an incident that took place at the Hippodrome, Constantinople’s great arena for chariot racing. Justinian was seated in the imperial box, surrounded by 50,000 racing fans, when one of them (no doubt equipped with a megaphone) engaged him directly in a debate about the nature of the incorruptibility of Christ’s body. The emperor and the fan went toe-to-toe on the issue in stanza after stanza of extemporaneous verse on the murkiest kind of Christian dogma, with occasional cheers from the crowd when one debater got in a good one. It was as if New York’s Mayor Bloomberg spent halftime at a Knicks game debating the finer points of string theory with a physicist seated twenty rows away, and not only did no one think anything extraordinary about it, but the drunks in the cheap seats applauded.

— William Rosen, discussing his fascinating book Justinian's Flea.