I've been on and off reading through the books on prehistory for the last couple of years, and now I want to somehow structure further reading. The goal is to get a good grasp on european/middle east history starting with invention of agriculture and up to around 500BC (for now), and also whatever epic literature is available. Here's what I've come up with, please help me fill out the blanks, suggest additional resources and/or better alternatives.
For Anatolia, I recommend combining Trevor Bryce's Warriors of Anatolia: A Concise History of the Hittites with Ancient Turkey by Antonio Sagona and Paul Zimansky. All of Bryce's books on ancient Anatolia are excellent, but he has always relied much more heavily on texts than archaeology, so the more archaeologically inclined volume by Sagona and Zimansky complements his history of the Hittites very nicely.
In the Land of a Thousand Gods: A History of Asia Minor in the Ancient World by Christian Marek is an excellent introduction to ancient Anatolia through the Roman period, but it is a rather dry read.
Van de Mieroop's history of Mesopotamia is an excellent place to start, as you've already discovered. I also recommend The Ancient Near East: History, Society and Economy by Mario Liverani. For Assyria and Babylonia specifically, see Ancient Assyria: A Very Short Introduction and A Short History of Babylon, both by Karen Radner.
Bottero's Religion in Ancient Mesopotamia is by far the best introduction to Mesopotamian religion, but The Treasures of Darkness: A History of Mesopotamian Religion is still well worth a read. Oppenheim's section on "Why a 'Mesopotamian Religion' should not be written" in Ancient Mesopotamia: Portrait of a Dead Civilization (free PDF) is also a classic.
Shaw's edited volume on Egyptian history is good but increasingly dated. Van de Mieroop's A History of Ancient Egypt and Wilkinson's The Rise and Fall of Ancient Egypt are used more often for Egyptian history courses these days. As a first introduction to Egypt, however, I recommend Temples, Tombs, and Hieroglyphs and Red Land, Black Land by Barbara Mertz. Also check out the excellent History of Egypt podcast, though it is currently only up to the 18th Dynasty.
Ancient Egyptian religion is a very complex subject, and no single book can do the subject justice. I provided a lengthy list of reading suggestions in a recent post.
As an alternative to Martin's book on ancient Greece, I recommend Edith Hall's Introducing the Ancient Greeks, which is a very engaging overview of ancient Greece that manages to incorporate a surprising amount of information without getting too bogged down in details.
It looks like your list includes quite a variety of texts, and that you’re interested in both primary and secondary sources, your list also includes both secular and religious works, so I’m assuming your interest in ancient history is in a more general sense (that is, you’re interested in politics, religion, and general lifestyles of ancient societies rather than just focusing on one aspect of history). There are quite a few books I think I can recommend related to your interest, some of these I have read, so I can confidently recommend them to you, some of them I have not read, but I believe they would still be relevant for what you’re looking for (titles in bold indicate texts I have read ,titles in italics are texts I have not read)
General History
Tom Head, World History 101 (general history of the world from the start of human civilization until the 2010s, target audience are readers who have little to no prior knowledge of history)
The History Book (similar concept to World History 101)
Mesopotamia
Enuma Elish (this is a Mesopotamian creation story, there are multiple versions of the story, the most common one to find is the Babylonian version. It contains the creation of the world and various gods, and the war in Heaven between Tiamat (the embodiment of chaos), and the head of the gods (in the Babylonian version, it is Marduk). Enuma Elish is a rather brief text, it is only about 40 or 50 pages).
Stephen Bourke The Middle East: The Cradle of Civilization Revealed
It should also be noted that there is more than one version of the Epic of Gilgamesh. When referring to the “Epic of Gilgamesh” it is usually the Standard Babylonian Version (c. 1300 BC) which is being invoked. The Standard Babylonian Version was written in the Akkadian language, and is a unified text chronicling the story of Gilgamesh from beginning to end. There are also, however, much older versions of the epic, the Old Babylonian Version, or Surpassing All Other Kings (c. 1800 BC) is another unified version of the story, the Old Babylonian Version, however, contains many more missing fragments than the Standard Babylonian Version. There are versions of Gilgamesh’s story even older than that, such as the ones written in the Sumerian language (its origins as far back as the third millennium BC), the Sumerian version of the story of Gilgamesh is contained in a series of seemingly unrelated tablets (differing the Sumerian version of Gilgamesh from the unified Babylonian versions). If you can only read one version of Gilgamesh, I would recommend the Standard Babylonian Version, but the older versions are also really useful to read if you wish to see how the Gilgamesh story developed over time.
The Bible (It is rather difficult to find copies of the Bible that only contain the Old Testament, even more so if you wish to also buy one with Dore’s illustrations. If you are interested in extending the historical time periods you are learning about, then I would recommend reading both the Old and New Testament. If you are only interested in learning about events before 500 BC (as your post implies) then the New Testament will likely not be very engaging to you (as it was written in and takes place entirely within the first century AD). The Old Testament is useful in learning about Ancient Near Eastern societies (especially Israel and Judah), it also contains a lot of information on the geography of Canaan (it should be noted, however, that the culture of the Canaanites, their religion, and practices, are not elaborated much in the Old Testament, it is quite clear that the authors of the Old Testament did not like the religion and cultural practices of the Canaanites, and so specific details of the lifestyle of the Canaanites are often exaggerated for the sake of presenting Canaan as evil. Though the King James Version (1611) is the most widely read English translation, the New Revised Standard Version (1989) is usually the modern academic preference. I would recommend reading a modern translation, as the King James Version uses archaic language that can be difficult to understand)
Egypt
Penguin Classics, Writings from Ancient Egypt (it’s what it sounds like, a compilation of various writings from the Old, Middle, and New Kingdom periods of Ancient Egypt. To my knowledge, the wrigins presented by Penguin are both secular (such as Egyptian accounts of the Battle of Megiddo against the Canaanites in 15th century BC) and religious (various hymns to the gods)
I would also recommend reading at least one version of the Egyptian Book of the Dead if you’re specifically interested in Egyptian religion
Greece
If you’re looking for general history, the writings of I would recommend the writings of Herodotus and Thucydides*.*
Herodotus’ Histories is quite fascinating, the main narrative is that of the Greco-Persian Wars in the 5th century BC, but the first half of Herodotus’ text is concerned with providing an extensive account on the rise of the Persian Empire (especially the life of Cyrus the Great), and the history and culture of various nations conquered by the Persian Empire (Herodotus dedicates the entirety of book two of the Histories to the geography, practices, and history of ancient Egypt, from its first Pharaoh, until the Persian conquest by Cambyses II). Herodotus provides a fascinating Greek perspective of the Persians, Scythians, and Egyptians. You should be cautious at times when reading Herodotus, however, as his history becomes much less reliable the farther back in time his narrative goes.
On the mythology side of things, the tragic plays of Aeschylus, Sophocles, and Euripides are a tremendous source of Greek mythology
Aeschylus’ Oresteia trilogy is the only complete Ancient Greek trilogy to survive (the trilogy tells the story of Agamemnon’s murder by his wife Clytemnestra upon his return from the Trojan War, the vengeance Agamemnon’s son Orestes takes against Clytemnestra and her accomplice, and the retribution Orestes faces for killing his own mother).
Sophocles’ Oedipus the King tells of the rise and fall of the Theban king Oedipus, Sophocles’ Antigone takes place after Oedipus’ death, and is about his daughter Antigone, who is in a moral dilemma, her brothers Eteocles and Polynices had killed each other as they fought on opposing sides of a war, though King Creon of Thebes allows Eteocles to be given a proper burial, he forbids the same burial for Polynices, as he fought against the king of Thebes.
Euripides’ Bacchae tells the story of Dionysus spreading his cult to Thebes.
I would also recommend reading some of Aristophanes’ comedies (though he was active slightly after 500 BC). Greek comedies, unlike tragedies, are based on original stories by the playwright, rather than stories from mythology. Aristophanes’ plays are full of political commentary and banter, all throughout his plays, Athenian politicians from his time are regularly named and criticized, Aristophanes is especially critical of those whom he perceives as having a bad influence on the youth (his play The Clouds contains the earliest surviving reference we have to Socrates, the philosopher is mocked throughout almost the entire play). I was surprised at how genuinely hilarious his plays are, they are also incredibly vulgar and offensive, if I were to compare Aristophanes’ plays to anything, they are like reading South Park scripts from 400 BC.