The Masters of Rome novels by Colleen McCullough are historically accurate, incredibly dramatic, gripping and realistic. They tell the story of Rome from the birth of Caesar in the Republic to the ascension of his successor Augustus in the Empire.
I, Claudius by Robert Graves is fascinating and very readable. One of the greatest examples of historical fiction. All of the major events of the book are historically accurate, and Graves just brings them to life with dialog and his knowledge of daily life in Rome. The sequel Claudius the God, is good, but honestly covers a less interesting period in Roman history.
Historically accurate-ish; she’s clear in her author’s notes that she created some characters to fill gaps. Would second the recommendation, though. The major events are generally real enough, and it’s a compelling way to read about it.