
As private secretary to the Emperor Hadrian, Suetonius gained access to the imperial archives and used them (along with carefully gathered eye-witness accounts) to produce one of the most colourful biographical works in history. The Twelve Caesars chronicles the public careers and private lives of the men who wielded absolute power over Rome, from the foundation of the empire under Julius Caesar and Augustus, to the decline into depravity and civil war under Nero, and the recovery and stabilitythat came with his successors. A masterpiece of anecdote, wry observation and detailed physical description, The Twelve Caesars presents us with a gallery of vividly drawn - and all too human - individuals.
Alternatively, you can get books about specific periods, like say late republic, and read those in sequence. But that takes more time.
Finally, and this is my preferred approach, get things written by Romans. Yes, they were biased too, and often quite obviously. But at least they didn't have stake in modern society and politics. As long as you pay notice to fact that they are mostly recording either hearsay, or propaganda, you should be fine. In that course I would recommend Twelve Caesars by Suetonius (hearsay) and Commentarii de Bello Gallico by Caesar (propaganda).
It's not always true, but it gives you a good idea of how they were thinking, what was their morality like and their values.
"The violent death of Caligula [the previous emperor] afforded the Romans a fresh opportunity to have asserted the liberty of their country; but the conspirators had concerted no plan, by which they should proceed upon the assassination of that tyrant; and the indecision of the senate, in a debate of two days, on so sudden an emergency, gave time to the caprice of the soldiers to interpose in the settlement of the government.
By an accident the most fortuitous, a man devoid of all pretensions to personal merit, so weak in understanding as to be the common sport of the emperor’s household, and an object of contempt even to his own kindred; this man, in the hour of military insolence, was nominated by the soldiers as successor to the Roman throne."
