Before even buying a book about the Bible, the first step is to buy a well-reputed study Bible. The Catholic Study Bible, the New Oxford Annotated Bible, or the Harper Study Bible are excellent Bibles for both prayer and study. The advantage these Bibles have is that they have well-documented footnotes and cross-references, introductory material before each book of the Bible, and they include maps and timelines.
An introduction to the Bible for very beginners is God’s Library: A Catholic Introduction to the World’s Greatest Book by Joe Paprocki. It teaches how to locate certain books in the Bible, how the numbering system and abbreviations work, and how to sort out “fact” from “fiction.” For something more in-depth (approximately at the college introductory level) you might look for An Introduction to the Bible: A Journey into Three Worlds by Hauer and Young.
A comprehensive and renowned commentary that addresses every chapter of every book in the Bible is The Jerome Biblical Commentary by Brown, Fitzmyer and Murphy. The price is hefty, but if you only want to own one book on the Bible, it is an excellent choice.
Beyond these specific suggestions, you might browse the shelves of a local university bookstore to see what the current required reading is for biblical courses.