Just a couple of quick thoughts:
First an apology. I love this stuff, so I'm sure this response is going to go way too long.
Now, as to extra-biblical sources from the ANE: sources before and contemporary with the writing of the books of the Bible are critical to understanding the biblical text. Context is everything in Bible translation especially when translating the Genesis creation stories. Translations that do not take into account the cultures and world-views of those days are not credible. Period.
Here are four examples of how ANE literature provides context:
In the pagan cultures of the ANE, time is thought to be tethered to nature and, therefore, cyclic. In Genesis 1, time is not cyclic. It is represented as linear, never-ending and never repeating. Unlike the other ANE cultures, the ancient Hebrews believed that one was accountable for one's actions in the past. The other cultures did not believe this as a matter of religion. Rather, in their view "time" started over in the new year and, provided a sufficiently large and earnest sacrifice was made, all was well again. This way of looking at time has profound moral consequences. In Ground Hog Day, for example, Bill Murray's character became a hedonist and a thoroughly detestable fellow. What he did in the 'now' had no effect in the future.
Most ANE creation stories of which I am aware have a "Tree of Life" in which the protagonist remains immortal so long as s/he as access to, and eats from, the Tree. Once access to the source (be it a tree, or well, or spring, or sea weed) s/he once again becomes mortal. In this context, expulsion from Eden means a loss of immortality and eventual death. Loss of access to the Tree of Life was widely and immediately understood as a loss of immortality.
Of all the creation stories ever studied no Tree of Knowledge of Good and Evil exists. The concept behind the Tree of Knowledge exists nowhere outside of Genesis. Now, in these other creation stories, loss of immortality is not associated with human misbehavior as much as it is associated with misfortune and circumstance. With this context in mind, the Genesis author uses the Tree of Life motif as a plot device to show that their expulsion resulted, not from circumstance like the other stories, but from a willful disregard for God's will. The author intended, I think (along with the scholars I cite in my translation) that to willfully disregard God's will results in separation from the divine.
In no other ANE creation story is the creation of woman even mentioned. But in Genesis all that changes: in Genesis 1 she is given equal weight with the man - including the command to rule creation. In Genesis 2, she gets 6 verses whereas the man gets only a part of one verse. Moreover, in Genesis 2 it is the husband who bears all the responsibility for her well-being and is the one who must stand-by his wife no matter what. In the ANE context where women are an afterthought, the elevation of the woman as a civilizing force on human society is remarkable.
Those are just four aspects of the creation stories whose meanings are profoundly influenced by competing ANE creation accounts.
Finally, I have at my desk a number of ANE books including Bottero's "Religion in Ancient Mesopotamia", Pilch's "A Cultural Handbook to the Bible", Podany and McGee's "The Ancient Near Eastern World", E. O. James' Myth and Ritual in the Ancient Near East: An Archeological and Documentary Study", and then a host of Bible commentaries which reference other ANE works. I also subscribe to Biblical Archeology - a magazine of 'popular' archeology, but that often cite some really interesting, more scholarly works.
Finally, all of my go-to Bibles are written and translated by the scholars themselves. In other words, these Bibles are commercially published, personal editions. I like these Bibles because they incorporate the latest research (and controversies). For example, I have Bray and Hobbins, Genesis 1-11, Alter's "The Five Books of MOSES - A Translation with Commentary", Friedman's Commentary on the Torah, E.A Speiser's Genesis, Sarna's Genesis edition of the JPS TORAH Commentary, Cassuto's Translation and Commentary "From Adam to Noah, The Book of Genesis, Robert Altar's among others.
Anyway, thanks for the interest.