Inspired by Tanner Greer, I’ve decided to put together a list of books that I think will useful to understanding the Romans from the perspective of a non-specialist without a background in Latin, or Classics more broadly (I am in this category obviously).
First, I’m a big fan of 
Robin Lane Fox’s The Classical World: From Homer to Hadrian covers a lot more than Rome, but what it does cover that is Greek is essential to understanding Rome.

There are so many nearly novel-like treatments of figures from the Second Triumvirate and the Julio-Claudians that I’m not going with anything conventional: try Agrippina: Sex, Power, and Politics in the Early Empire. Colin Wells’ The Roman Empire focuses on the imperial apogee and the early years of the 3rd-century troubles. It’s a bit pedestrian but has interesting quantitative data like the decline in the proportion of soldiers of Italian origin over the centuries. If you’ve read the survey above then you know why Gwyn Morgan’s 69 A.D.: Year of Four Emperors is important to read.

The Fall of Rome: And the End of Civilization, The Fate of Rome: Climate, Disease, and the End of an Empire, and The Fall of the Roman Empire: A New History of Rome and the Barbarians are all critical contemporary analyses of the end the Roman polity. Written from an archaeological, environmental scientific, and narrative historical angles, they give different viewpoints on the same questions. These are all more or less responses to the sort of work written by Peter Brown a generation earlier, The Rise of Western Christendom: Triumph and Diversity, A.D. 200-1000, which argues against the idea of the fall. From a different perspective (the barbarian), The End of Empire: Attila the Hun & the Fall of Rome, though to be frank this book is as much about Aetius as it is about Attila.

I’m not a humanist in Tanner’s league, so you won’t get poetry recommendations from me, but Aupelius’ The Golden Ass is the only complete surviving Latin novel. It’s rather weird. You surely know the list of eminences of the Latin poets, but Ovid’s Metamorphoses induced less labor than Virgil’s Aeneid. I recall thinking Virgil was a bit too “try hard.” Unlike The Fall of Rome: And the End of Civilization and History of Rome, both of which I’ve read more than half a dozen times front to back, with literature I usually read once, and don’t retain too much. I’m a Philistine!

Historical fiction isn’t always accurate, but it really brings the dramatis personae alive. Colleen McCoullough’s First Man in Rome series is excellent, especially the first few novels. Everyone knows Robert Graves’ I, Claudius. But my teenage-self really enjoyed Allan Massie’s Let the Emperor Speak, about Augustus, and Tiberius: The Memoirs of the Emperor. Gore Vidal’s Julian: A Novel is well written and engaging, though a little light on history (not surprisingly there is a lot of editorializing by Vidal through Julian).

Rodney Stark wrote The Rise of Christianity: How the Obscure, Marginal Jesus Movement Became the Dominant Religious Force in the Western World in a Few Centuries back when he was a scholar and not a polemicist. I’m skeptical of some of his conclusions, but his thinking here is rigorous.
Some of the New Testament is interesting too. I especially think that the material attributed to St. Paul, a Roman citizen, is worth reading closely.
And finally, St. Augustine is worth a read. City of God is interminably long, but Confessions is more compact, and the beginning of a whole genre which eventually culminated in James Frey.

I will pump for Gibbon’s “History of the Decline and Fall of the Roman Empire” I know that there has been a lot of scientific work done since the third most important publication of 1776, but the literary quality and scholarly comprehensiveness of the work are unchallenged. I would argue that it is the greatest prose work of the English language and should be read for that reason alone.
You can download it in 12 volumes with the JH Bury Notes from:
https://oll.libertyfund.org/titles/gibbon-the-history-of-the-decline-and-fall-of-the-roman-empire-12-vols
Note: that website has free and good editions of many classic works of history, politics, and economics. It is a valuable resource.
An Amazon link: https://www.amazon.com/Decline-Fall-Roman-Empire-Everymans/dp/0679423087
From a customer review there:
“I will append a single proviso to my five-star rating: to enjoy this book, you will need a somewhat decent command of the English language and the capacity to unpack dense meaning. Gibbon’s prose, to my mind, is almost without par; however, it is very much written in the Enlightenment style, which was more complex than what we accustomed to from today’s workman-like scribblers.”
While a mixture of ‘narrative story’ and historical fact viewing, ‘Rubicon: The Last Years of the Roman Republic’ was a informative journey.
What is often at display in Roman literature recommendation threads is how these popular works are always about the downfall, they’re not about rise of the empire. It’s nearly always the downfall. Odd bias there (?).
yes. weird bias. but i think that’s because the *end* has a clearer point than the *beginning* (and even the end isn’t as clear as 476).
Would you have something similar on the Mughals?
new heather book i just got Rome Resurgent: War and Empire in the Age of Justinian.
https://www.goodreads.com/book/show/31456148-the-holy-roman-empire
” The Holy Roman Empire: A Thousand Years of Europe’s History” might be of interest to you. A fella I follow in Twitter has posted very interesting excerpts of it, enough to make me add it to my (endless) backlog.