If you want academic, peer reviewed books, look at the publisher. Go for major academic institutions like Cambridge, Oxford, Indiana, Harvard etc. These books will be much more likely to be of academic quality than self-published or common consumption publishers. Most of these publishers have catalogs available on their websites.

Have you checked the book list?

I personally found 'A history of the Ancient Near East' by Van De Mieroop a good and readable introduction. I also liked how he accompanied the subject matter with relevant ancient historical sources of which context and translations are provided. It should be easy to get and shouldn't be expensive either. As a classical historian I can't discuss correctness but the writer teaches (or teached?) at the university of Oxford and it's published by the reputable Wiley-Blackwell. It covers mostly Mesopotamia but also the Levant and other neighbouring regions when relevant. It spans from the beginning of Mesopotamian civilization up to Alexander the Great.