You're welcome. While it's not among the standard recommendations at the top of the list, if you've never read anything about Mesopotamia before I would actually suggest starting with:
Gill, Anton. 2011. Gateway to the Gods: the Rise and Fall of Babylon. Quercus Publishing Plc.
The book covers the entire history of Babylon, with some introductory sections about Sumer and Akkad to set the scene. It also has several chapters at the end that discuss cultural aspects like art, magic, religion, etc. But, the real benefit, in my opinion, is the wealth of pictures throughout the chapters covering each historical period.
It also has one of the few write-ups about the Neo-Babylonian Empire that tries to understand the motivations behind King Nabonidus' actions, rather than just painting him as an insane king who did things because he was crazy, which I found quite refreshing.