Reddit reviews Introduction to the Bible (The Open Yale Courses Series)

These Yale Religious Studies lectures are a fantastic introduction to critical scholarship. The OT series is particularly well done and this lay reader would think they'd give you all the background you need to explore topics more in depth on your own. IIRC, the OT series has the JPS study bible as recommended reading, which would also offer introductory essays for each biblical text.

If you have your heart set on a book, you would probably be best served by a proper introductory textbook, but FYI they do have the material from these courses in book form. The OT one reads pretty much like a transcript of the lectures, while the NT professor said he had to recreate the text from the ground up because of how freeform his lectures are ;)

There's also an associated book for that course.

This is the accompanying textbook for Yale's excellent Old Testament introductory course by Christine Hayes.