I Claudius and Claudius the God by Robert Graves are classics for a reason and really set the standard for fiction set in this Era, a great telling about the political machinations of August and his extended Family covering the first four emperors.
The first man of Rome series by Coleen McCullough is fantastic - It runs from Marius and Sulla (the generation before Julius Caesar) up to the start of Augustus, great storytelling of actual history.
I second the Falco books by Lindsey Davies
Corvinius Series by David Wishart. The first 3 especially - Ovid, Germanicus and Sejanus, work as a trilogy and then the rest are fun mysteries with the same PI character, similar to the Falco approach.
The Roma sub rosa series by Steven Saylor - again, a detective working in the thick of real historical events of Republican Rome.
None of them are particularly adult in the sense of sexy, although they are about events that include all human behaviour, which occasionally includes sex. No Jackie Collinsstyle graphic descriptions, though.🙂