Reddit mentions of The Roman World 44 BC-AD 180: Second Edition (The Routledge History of the Ancient World)

I found this interesting: it's up to date and 'undergrad textbook' style if that makes sense!

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Starts a bit earlier but to be honest just reading the early historians will give you a skewed view anyway: they have their own slant, it's missing archaelogy etc. So this will buttress those with something more robust (incidentally, though Gibbon was a fantastic historian at his time and helped develop improvements in method, he's also somewhat out of date in a similar way and you might want to consider instead/alongside reading him reading books that reflect latest archaeology and techniques.

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The Roman World 44 BC-AD 180

If you're really an enthusiast and can afford to build yourself a nice collection, you could look into getting some Loeb Classical Library volumes which have the Latin original on one side and the English translation on the other. Others have already suggested Livy, Suetonius, Juvenal and Julius Caesar, though as I said, if you're an enthusiast, they will all be of value. I'd add Tacitus and Pliny also for good measure.

"From the Gracchi to Nero: A History of Rome 133 BC to AD 68" by H.H. Scullard has been recommended, though it doesn't (entirely) cover the period you're interested in, it's very good in explaining the lead-up to the Roman Empire. I'm not sure about other's views on Scullard, so best to ask them.

Edward Gibbon has already been mentioned, I'd probably also add Colin Wells' "The Roman Empire", A. Cameron's "The Later Roman Empire" and M. Goodman's "The Roman World 44 BC-AD 180".

Best of luck with everything and congratulations on your new house!