I adore watching the show Rome, and get lost reading about the various rulers on Wikipedia. I would love to get more in depth with the history. Straight historical literature can be a bit dry for my taste, so something a bit engaging would be nice. I also am a huge fan of historical fiction, so if there happens to be some great works on the Roman Empire that are historically accurate with the added fictive, then I'd be interested in that too.
One good place to start would be the AskHistorian's book list on ancient Rome.
To this I might add the Cambridge Ancient History series. This is broken down into different periods, so if you are interested in the end of the Republic, for instance, you could check out volume 9.
The Empire series by Anthony Riches is amazing. Its Historical fiction similar to that of the Eagle series by Simon Scarrow, another great series.
Well, if you liked Rome the series then there's a book that covers almost that exact period and does a damn good job of explaining the rise and success of Octavianus/Augustus. The downside is that it's that type of 'dry' literature you're not a fan of. Try to get Syme's The Roman Revolution from a library and try a chapter or two to see if you like it. Personally I really enjoyed it and felt he did a great job explaining how some obscure teenager became the absolute ruler of the Roman empire.
I would strongly recommend Tom Holland's Rubicon (2003), a popular history that tells the story of the final years of the Roman Republic and founding of the Empire, and so fits quite well with the period covered in HBO's Rome series. It's well-written and engaging; I used to include it as recommended summer reading for students entering my Pre-AP Latin course. Holland has also recently published a book on the first emperors of Rome called Dynasty: The Rise and Fall of the House of Caesar, which I have not read yet, but if it's anything like Rubicon it should be worth the read.
If you're interested in how the Romans succeeded to create such a vast and powerful empire from relatively meager beginnings, I would suggest Mary Beard's recent book, SPQR: a History of Ancient Rome (2015). Here is a great review by the Atlantic of Beard's methods and work.