Start where writing starts
Babylon · Paul Kriwaczek (2010)
Mesopotamia from Sumer to the fall of Babylon, which is where cities, writing, law codes and astronomy all begin and which almost nobody reads about. Kriwaczek is a journalist rather than an academic and it shows in the pace, which for a first book on Sumer is exactly what you want.
The Epic of Gilgamesh · translated by Andrew George (1999)
The oldest surviving great work of literature, about four thousand years old, and still about the thing it was always about: a man who cannot accept that his friend died and that he will. George's translation shows the gaps in the tablets rather than smoothing them, which makes it feel excavated instead of retold.
Then Egypt
The Rise and Fall of Ancient Egypt · Toby Wilkinson (2010)
Three thousand years as a political story rather than a mystery. The full Egyptian shelf, including the gods and the funerary texts, is on our ancient Egypt page.
Then Greece
Introducing the Ancient Greeks · Edith Hall (2014)
Ten chapters organised around what made the Greeks distinctive rather than a march through dates, which is the right shape for a first book. Then Herodotus, who invented the genre and remains the most entertaining practitioner of it. More on the Greek history shelf.
Then Rome
SPQR · Mary Beard (2015)
A thousand years of Rome in one argued volume, stopping at 212 AD rather than dragging you through the decline. The Republic's collapse and the Empire's are both covered on the Roman shelf.
Then the East
China: A History · John Keay (2009)
The half of the ancient world that Western reading lists routinely omit, running from the Shang bronzes onward. Han China and imperial Rome were contemporaries of comparable scale and knew almost nothing about each other, which is itself worth sitting with. See the Chinese history shelf.
How the ancient world connects
The mistake in reading these as separate subjects is that the ancients did not. Persia links Mesopotamia to Greece; Alexander links Greece to Egypt and India; the Silk Roads link Rome to Han China. Peter Frankopan's The Silk Roads (2015) is the book that reorganises the whole picture around that traffic, and it belongs on this shelf as soon as the individual civilisations have names attached.
Fitting the ancient world into a real life
Five civilisations and four thousand years is not a fortnight's work, and enthusiasm reliably dies in the middle of the second book. A daily page keeps the map warm while the big books go slowly: 365 Days of World History (ours, flagged) runs one day in history per day across the entire record, and 365 Days of Mythology covers the stories these societies told about themselves. The world history shelf holds the single-volume overviews.
Common questions
What is the best book on ancient history for beginners?
There is no single one, because the field is five separate literatures. Start with the civilisation that already interests you: Wilkinson for Egypt, Hall for Greece, Beard for Rome, Kriwaczek for Mesopotamia, Keay for China.
Where does ancient history actually begin?
With writing, in Sumer, around 3200 BC. Everything before that is prehistory and read through archaeology rather than texts, which is a different kind of book.
Should I read the ancient sources or modern historians first?
Modern historians first, almost always. Herodotus and Sima Qian are far more enjoyable once you know roughly what happened and who the names belong to.
What connects the ancient civilisations to each other?
Trade and conquest, mostly. Peter Frankopan's The Silk Roads is the best single account of the traffic that linked Rome, Persia, India and China.