I recently got Mary Beard’s ‘SPQR: A History of Ancient Rome’ because I wanted a book that explained...well, the history of Ancient Rome.
So far as I have read, my views on the book are more negative than positive. because of the way it was written.
I don’t know how to describe it, but I find the language of the book is something along the lines of being waffley & too conversational.
I prefer history books which just explain the history almost like a textbook (ie events, what life was like, causes, results etc) rather than putting forward an argument or trying to be conversational. Essentially, stick to the point.
Example of books I have which are good examples are: -‘A History of the Modern Middle-East’ by William L. Cleveland & Martin Bunton -‘The Holocaust: A New History’ by Lawrence Rees
So is there a book on Ancient Rome that has the following: —Covers the history, preferably from Rome’s founding to its fall in 476/480 CE; —Just explains (or ‘story tells’) the events, like the books I mentioned above (preferably ‘A History of Middle-East’), rather than be conversational.
Its worth checking out the reading list and seeing if any of those fulfill your needs.
https://www.reddit.com/r/AskHistorians/wiki/books/europe#wiki_ancient_rome
From a personal perspective I find that books on Rome from start to fall (without even getting to Byzantium falling in 1453) are generally to broad brush to be enlightening, a lot happened in a lot of different areas and most of the all in one books tend to go over the same material over and over again without really giving you an indepth picture because they don't have time to do so.
I would pick an area that interests you, the rise, the fall, what Gaul/Britannia/Egypt/Germania was like in the period, books on an interesting period/Emperor and focus on that.
You might give Michael Grant's History of Rome a shot. The prose is clean and his audience is the general reader. The list chiron3636 links to is good, but he's right, there's a lot of material to cover and squeezing it into one book is a challenge. Still, go for Grant for now, I think he should suit your criteria.
Alternatively, Mary Boatwright's The Romans From Village to Empire: A History of Rome for Earliest times to the End of the Western Empire is the standard intro textbook these days.
Robin Lane Fox’s ‘The Classical World’ is excellent, though it covers both Ancient Greece and Rome.