bro, i fell asleep
sorry bro, didn't read that. well, while i was in uni, we didn't read many books per se LOL. it was compulsory for us to take classes from hittitology and archaeology (archeo of old, middle, neo-assyria, babylonia, akkad, glyptics/cylinder seals, prehistorical archeo of near east) and we learned a lot about history of the region from these classes. and we had a lot of classes like texts/letters of specific periods where our teachers (two of them are the guys who excavate and read cuneiform tablets from kültepe/kanesh
Kültepe - Wikipedia, the free encyclopedia ) would tell us details you won't find in any source. for you i can recommend s. noah cramer's history begins at sumer (which has a huge "for further reading" part in the end) and the cambridge ancient history series. oxford also has good books on the subject and i had a list of books from their publishing house but couldn't find it now.