I would recommend starting with the Jewish Study Bible (the JPS translation is good).
The OT is a library of various genres of literature. It really depends on what books you want to apply criticism to, and what form of criticism you want to apply. Do you want to do comparative criticism of the Genesis account? Then I would suggest starting with the JPS and a copy of the Babylonian creation story. The Israelite laws? Then get copies of the Middle Assyrian laws, the code of Lipit-Ishtar, the code of Hammurabi, and the Hittite laws. Are you looking to do redaction criticism? Historical criticism?
Or are you looking for books that have done the footwork already to explain the criticism itself? If that's the case then I can't really help, OT isn't my forte. I'm sure that someone will have a good suggestion though.
History of Old Testament Criticism by Archibald Duff.
I hope you like it.
The Old Testament?
This one is by a liberal theologian... but it basically tears the literal bible to pieces:
"Rescuing the Bible From Fundamentalism"
OMG!! I forgot!! This is the best book EVER for dismantling either testament!
THE BIBLE HANDBOOK https://atheists.org/store/index.php?main_page=product_info&cPa...
Don't let the Bible-spouters snow you! A good offense is the best defense. The Bible Handbook is actually three books under one cover - books you can't afford to be without when under supernaturalist assault. The first part of this manual bears the volume title and is by G. W. Foote and W. P. Ball. It is divided into the sections "Bible Contradictions," "Bible Absurdities," "Bible Atrocities," "Unfulfilled Prophecies and Broken Promises," and "Bible Immoralities, Indecencies, and Obscenities." The second part is a book entitled "Self-Contradictions of The Bible: 144 Propositions," by that famous author Anonymous. The third part is the book "The Bible Contradicts Itself," by John Bowden. In addition, there is an Introduction by Jon G. Murray, a Foreword to the First American Edition by Madalyn O'Hair, and an American Atheist Addendum on absurdities and contradictions.