Some background: I am a PhD student in economics; I have taken a lot of history and archaeology courses in college and read a lot as well. However, I wasn't very systematic; I constantly started new books and read half of each. Also, I used to skip most numbers (dates included) and never check maps. So, I always get confused about when a civilization existed, whether two of them coexisted or shared "border", etc. Now I have decided to fix this. My eventual goal is to teach myself about the histories of Europe and Near East from the prehistoric era to today. (I mean, eventually all around the world but I'm starting from where I am close to.) Based on the reading lists here and elsewhere, I have compiled the readings listed below for this purpose. However, I still have some missing pieces to fill and questions about the order of readings.
I thought I would start with the Near Eastern, Greek and Roman histories until the beginning of the medieval period. (I am planning to read about 40-50, (at most 60, if possible) books in next 3 years on this plan to give an idea about the "budget".) My focus is to learn about political, economic and social histories, with about equal importance. Of course, if a society has more influence on the other civilizations in a particular topic or something like that, I wouldn't mind increasing the weight of that topic for this society to dig a little deeper. (I am not particularly interested in art history right now.)
Obviously, I left out many regions and eras. I am looking for resources to fill the gaps. I don't have anything particular to read about Celts, Etruscans, Assyrians and German tribes so I want to add whatever you historians can suggest on these. (Books suggested on these topics before seem to be either too superficial or too specialized; I was looking for something in between.)
What other societies I should have included but haven't for a good enough picture of this era in these regions? Also, what can I read about the prehistory? I have read The Horse, the Wheel, and Language by David Anthony recently but it naturally has a limited scope. If there was one or two books that can give a good overview of prehistory of Europe, that would be really helpful. (I am kinda assuming prehistory of Anatolia and around would be covered in the books in about that region but if not, then I will need something for that area as well.)
I haven't included the primary sources or earlier historians works on this list but I will to read them as supplements after familiarizing myself with the contexts of the texts. I will basically put the reading lists of some Classics departments together and try to read them. (Also, I want to read at least Latin sources from the originals, so I have to brush up my Latin and hopefully learn some Greek later.) However, if there are some important primary sources that are less well-known or not commonly included in the schools' reading lists, I would be happy to add them on a parallel list.
Finally, there is the issue of where to start and how to continue: My plan initial plan was to read them in regional order; Near Eastern, Greek and Roman history. However, considering coexisting societies and their interactions, I am not sure if this is the right course. If someone can make any suggestion about the order in which I should go, that would be really helpful. For example, Phoenicians, Babylonians, Carthaginians and Egyptians all had some shared history with Greeks. What would be the correct order to read about them? If the influence of the interaction is mostly one-sided, then it would make sense to start with the 'influencer', then the influenced but I am sure the relations were more complicated than that; so I couldn't make up my mind here.
Near Eastern:
The Ancient Near East: History, Society and Economy by Mario Liverani
A History of the Ancient Near East, ca. 3000-323 BC by Marc Van De Mieroop
Sumer and the Sumerians by Harriet Crawford
The Kingdom of the Hittites by Trevor Bryce
Life and Society in the Hittite World by Trevor Bryce
The Phoenicians and the West: Politics, Colonies and Trade by Maria Eugenia Aubet
A History of Babylon, 2200 BC - AD 75 by Paul-Alain Beaulieu
Carthage: A History by Serge Lancel
Ancient Israel: What Do We Know and How Do We Know It? by Lester L. Grabbe
Israel's History and the History of Israel by Mario Liverani
A History of Ancient Egypt by Marc Van De Mieroop
Egypt in the Age of Cleopatra: History and Society under the Ptolemies by Michel Chauveau, David Lorton
The Oxford Handbook of Ancient Iran (Oxford Handbooks) by D. T. Potts
Arabia and the Arabs: From the Bronze Age to the Coming of Islam by Robert G. Hoyland
Greek:
Trojans and Their Neighbours: An Introduction by Trevor Bryce
Greece in the Bronze Age by Emily Vermeule
Greece in the Making, 1200-479 BC by Robin Osborne
The End of the Bronze Age by Robert Drews
A History of the Archaic Greek World, ca. 1200-479 BCE by Hall
The Greek World 479-323 BC by Simon Hornblower
Archaic Greece: The Age of Experiment by Anthony M. Snodgrass
A History of the Classical Greek World: 478 - 323 BC by P. J. Rhodes
Alexander to Actium: The Historical Evolution of the Hellenistic Age by Peter Green
The Greek World After Alexander 323-30 BC by Graham Shipley
The Rise and Fall of Classical Greece by Josiah Ober
Alexander the Great in His World by Carol G. Thomas
Goddesses, Whores, Wives, and Slaves: Women in Classical Antiquity by Sarah Pomeroy
(Probably later in life, when I am retired or something) History of Peloponnesian War series by Kagan
Roman:
The Roman Revolution by Ronald Syme
Mediterranean Anarchy, Interstate War, and the Rise of Rome by Arthur M. Eckstein
Ancient Rome: A Military and Political History by Christopher S. Mackay
The World of Late Antiquity: AD 150-750 by Peter Brown, Geoffrey Barraclough
The Fall of Rome: And the End of Civilization by Bryan Ward-Perkins
How Rome Fell: Death of a Superpower by Adrian Goldsworthy
Troy between Greece and Rome: Local Tradition and Imperial Power by Andrew Erskine
Pompeii: The Life of a Roman Town by Mary Beard
Emperor Worship and Roman Religion by Ittai Gradel
(For fun) Mommsen and Gibbon
If you haven't seen it yet, take a look at the AskHistorians reading list, which contains a section on Assyria. There is also the MOOC Organising an Empire: The Assyrian Way, taught by Karen Radner.
I recommend beginning with Ancient Near Eastern History and Culture by William Stiebing and Susan Helft, which is the best single-volume introduction to Egyptian and ancient Near Eastern history that I've come across. Coverage of each period is relatively superficial since there's so much material to cover, but it provides a solid foundation for further reading.
For a more detailed overview of ancient Near Eastern history, the books by Van de Mieroop and Liverani - already on your list - are quite good. One could add Postgate's Early Mesopotamia: Society and Economy at the Dawn of History for the first half of Mesopotamian history.
There are quite a few popular introductions to ancient Egyptian history. I personally prefer Van de Mieroop's book, but many people like The Rise and Fall of Ancient Egypt by Toby Wilkinson. Temples, Tombs, and Hieroglyphs: A Popular History of Ancient Egypt by Barbara Mertz is very good and a lively read; the companion volume Red Land, Black Land: Daily Life in Ancient Egypt is excellent as well.
Trevor Bryce's The Kingdom of the Hittites and Life and Society in the Hittite World are still some of the best introductions to the Hittites in English. His new book Warriors of Anatolia: A Concise History of the Hittites is a bit of a mishmash of the two, and it's now the book I recommend as a first introduction to the Hittites. I keep forgetting to add The Hittites and Their World by Billie Jean Collins to the AH reading list, which is another very good overview of Hittite history and society.
Vermeule was a brilliant scholar, but Greece in the Bronze Age is now woefully outdated. For Bronze Age Greece, begin with Minoans by J. Lesley Fitton and The Mycenaeans by Louise Schofield. The Oxford Handbook of the Bronze Age Aegean and The Cambridge Companion to the Aegean Bronze Age are more comprehensive but not as readable or well-illustrated. Cyprian Broodbank's The Making of the Middle Sea is a superb introduction to the ancient Mediterranean in general.
Drews' book on the end of the Late Bronze Age is also outdated. Guy Middleton's Understanding Collapse and Eric Cline's 1177 BC have good discussions of the issues surrounding the end of the Bronze Age.
A History of Ancient Israel and Judah by James Miller and John Hayes is an excellent introduction to the history and archaeology of ancient Israel. Even by the standards of academia, this is a field in which there is very little consensus, however.
If you're interested in the economies of ancient societies, I recommend starting with these:
The Ancient Egyptian Economy: 3000–30 BCE by Brian Muhs
The Fundamentals of Economics: Lessons from the Bronze Age Near East by David Warburton
Ancient Kanesh: A Merchant Colony in Bronze Age Anatolia by Mogens Larsen
Aspects of the Economic History of Babylonia in the First Millennium BC by Michael Jursa
This is barely scratching the surface of what's out there, but it should be enough to get you started.