Someone else could give you a more focused answer, but if you're looking to expand your library, you can always check out our recommended reading booklist. (I've linked to the Ancient Greece section, and Ancient Rome is right underneath.) Seems to be close to 100 books on the topics (possibly even more), organized both chronologically and by topic, so it should be a good place to get started.

I would definitely second the recommendation of this sub’s book list, as well as sources cited in specific answers on askhistorians that interest you. The recommendation of Mary Beard in that list is at least a recommendation I see very very commonly echoed. My interest is not quite the Rome-focused literature you seem interested in, but there are some useful practices for the environment of academic writing/reading I can hopefully share.

Firstly, check footnotes or endnotes. Not necessarily all the time, but when a specific passage seems potentially meaningful, interesting, or controversial you will very likely be able to find something new to read directly cited in the notes. Paying attention as you read and picking out passages to follow up on is good practice anyway. I keep a list of works I might be interested in reading myself with notes on where I first saw them cited. Most responsibly written academic books also devote sections of the main text to explaining researchers and specific secondary sources which contribute to the academic background of the topic in question. Look into following up with some those works, especially if the author indicates there are good-faith, current academic disputes over a topic. Citations can also help you evaluate the merits of whatever work you are currently reading. There are valuable books written by academic historians nowadays that consciously eschew footnotes to reach out to the wider population, but make sure these at least have a well-organized general bibliography of recent secondary sources. Even so, I still think a substantially sized section of notes and citations after the end of the main text is preferable.

Also, pay attention to names. Someone with a university posting publishing monographs through academic presses in your field of interest almost certainly either has published or will publish much much more in that field. It’s generally worth looking at the other output of the people who wrote at least one widely cited work in your area of interest. Best case scenario is if you find a respected author writing on a topic you like who also recently (co-)edited or contributed to an edited volume. These combine chapters written by many academics who the editors think are doing valuable work. This means you can get a variety of topics, perspectives, and most importantly a wide-ranging bibliography from a single (admittedly often expensive) book. These also generally have a good summary of the current historiography of the topic in one of the chapters, and give you a good idea of the respected names in the field by way of the chapter author list, so you can follow up on those too.

You may have noted that this advice will likely provide you with a reading list organized by topic, and not as much chronologically. This is probably a good thing. Academic works obviously cover a specific time frame, but you should probably think of them more as analyzing a specific topic through a specific lens (over a specific period). For instance Rome Enters the Greek East: from anarchy to hierarchy in the Hellenistic Mediterranean, 230-170 BC by Arthur Eckstein is a book about Roman expansionism in the eastern half of the Mediterranean world which analyzes Roman behavior through the lens of modern International Relations theories of state behavior and happens to use 230-170 BCE as the time period for its case study. It is not intended to be read immediately after a hypothetical book covering Roman religion from 300-230 BCE. As another example, the Roman founding myths you might be interested in as a beginning to your studies don’t really just involve a single point in time. Studies of Roman founding myths might look at how Romans and others understood and portrayed those myths in periods after the founding of the city, how the myths told changed over time from the early republic out through the Christian portions of Roman history, and what antecedents from before the Roman period might have caused the stories to develop as they did. It will probably profit you more to sort your reading by topic so you can compare the methods and conclusions of different studies, even if they cover slightly different time periods. This may be more revealing of interpretive differences or change over time than reading indirectly related works which happen to cover similar or adjacent year brackets.