As you can probably imagine, Roman history stretches for a very long period of time with a variety of topics that one could read about which can make it difficult to recommend books.

The Cambridge Ancient History series (Volumes 7-13 stretches from the foundation of Rome to the period of the Late Empire - each volume focussed on a different time period) is very good because it provides a general introduction to 'general' scholarship on different facets of Rome. You could use such books to get an idea of what it is exactly you want to read about.

I'll recommend some general books too for topics of some interest:

Bispham, E.H., T.E.H. Harrison, B.A. Sparkes (edd.) (2006). The Edinburgh Companion to Ancient Greece and Rome. Edinburgh.

• Again, like the Cambridge Ancient History series it is a generalised book on a variety of topics that would provide insight into general themes.

Harris, W.V. (1985). War and Imperialism in Republican Rome, 327-70 B.C.. Oxford.

• A book that makes an argument that Rome infact was not defensive, but the aggressor. At the time of publishing it was influential book because the consensus at the time was that Rome was a defensive state. Later books have been published with criticism and alternative views which offer further interpretations of the topic.

Kay, P. (2014). Rome’s Economic Revolution, Oxford.

• A good book on Rome's economy between the Second Punic War and the first century B.C.

Syme, R. (1939). The Roman Revolution. Oxford.

• Really good book on the transformation from the Roman Republic to the Roman Empire - outdated now but definitely paved the way for a lot of future research on the topic.

If you have any idea of what it is exactly you want to read about or research further, I can always recommend more books based specifically on that. This list however I would say is a pretty good start, especially the Cambridge Ancient History series. I would also say on your plan to approach studying Roman history based upon a syllabus from the early 20th century to not do it - a lot has changed since then with the revealing of new evidence and new studies, you would get a greater understanding of the topic from later books.

As the Romans Did: A Sourcebook in Roman Social History is a common text for basic Roman history courses. I have both editions but couldn't specifically tell you the difference, I think the second edition has more material. It's not an overarching narrative of Roman history or anything like that, it's kind of a "slice of life" selection of primary texts that show how some Romans at some points of history lived. I'd recommend it as an introduction since you said you didn't know where to start, and (1) primary sources are always a great way to get a feel for a period, and (2) you can figure out which elements of Roman history/culture most interest you and dive into other, more specific texts and sources from there.

Personally, I'm very interested in the institution of Roman slavery, and so could give a few recommendations there.

(Unfortunately, I don't have anything like an early 20th century Roman history syllabus, but that sounds interesting. I hope you find one. Obviously historical thought on Rome has evolved greatly since then, and it would be cool to see that directly.)