An annotated list of selected books, followed by an extensive bibliography.

For a quick, simple and basic overview of the Hebrew Bible in its historical context, with maps and chronologies as well as brief introductions to the sections of the Hebrew Bible:
—-  Hupping, Carol, and et al, eds. The Jewish Bible: A JPS Guide. Philadelphia: Jewish Publication Society, 2008.

The Hebrew Bible in English, with introductions to each Section and each book, as well as many essays about the Bible.   This is an all-English edition.  If you don’t need Hebrew, and you only want to buy one book – this is it.
—- Berlin, Adele, and Marc Zvi Brettler, eds. The Jewish Study Bible: Second Edition. New York: Oxford University Press, Inc., 2014.

The standard JPS Hebrew-English Bible – with no commentary.   This book is the one to get if you want Hebrew.  If you want commentary, pair it with The Jewish Study Bible.
—- JPS Hebrew-English Tanakh: The Traditional Hebrew Text and the New JPS Translation. Second. Philadelphia: Jewish Publication Society, 1999.

Two books focusing on the place of women in the Bible:
—-Frymer-Kensky, Tikva. Reading the Women of the Bible: A New Interpretation of Their Stories. New York: Schocken Books, 2002.

—-Newsom, Carol A., and Sharon H. Ringe, eds. The Women’s Bible Commentary – expanded. Louisville, KY: Westminster John Knox Press, 1998.

Two books giving alternative translations for Samuel 1 and 2 with some commentary:

—-Alter, Robert. The David Story: A Translation with Commentary of 1 and 2 Samuel. New York: W.W. Norton & Co., 1999.

—-Fox, Everett Dr. Give Us a King!: Samuel, Saul, and David. New York: Schocken Books, 1999.

This very interesting book on David should be read only after you have studied the original.
—-Pinsky, Robert. The Life of David. New York: Schocken Books, 2005.