I had the same issue. My problem with most study material that I could find was that it was written from the fundementalist perspective (what the Bible say is meant to be literally true). Finally I found and bought the The HarperCollins Study Bible : New Revised Standard Version With the Apocryphal / Deuterocanonical Books because it has notes written by biblical scholars that point out context and other information that get's overlooked or ignored by others.

This book from the UUA bookstore would be a good start. I was raised a fundamentalist Christian and so know quite a bit about it, but when I read this book, I thought it was a nice summary:
secure.uua.org/bookstore/...ct_info.php

Understanding the Bible
An Introduction for Skeptics, Seekers, and Religious Liberals
John A. Buehrens
Beacon Press
6170

Understanding the Bible

Designed to help empower skeptics, seekers, nonbelievers, and those of a liberal and progressive outlook to reclaim the Bible from literalists. Includes four preliminary chapters on the why, who, which, and how of bible understanding, followed by eight brief thematic chapters covering the core of the Hebrew Bible and six covering the Christian scriptures, plus chronologies, maps, and helpful suggestions for further reading. (Beacon) 2003 224 pp. ISBN: 0-8070-1053-7

I second the recommendation for the Harper Collin's Study Bible. It's in accessible language, but isn't dumbed down. It's also academincally rigorous, so you don't lose the "intent" of the original language as much as you do with some of the published works that just want people to be familiar with the stories.

John Buehrens' book is also a good suggestion.

I would recommend "The Old Testament: An Introduction to the Hebrew Bible" by Stephen Harris and Robert Platzner, as a companion to reading the OT. It is written like a text book, but also very easy to understand and addresses many key ideas and historical contexts. I am currently reading it for an OT Foundations course, and have really appreciated it.

The most interesting (and funniest) translation I have seen to date is the LOL Cat Bible: www.lolcatbible.com . Blame Shakesville contributor The Portly Dyke for introducing me to this wiki gem. If you don't get the whole LOL Cat phenomenon, though, don't bother.

Sorry, no serious suggestions, as I have never given the Bible the time and effort I perhaps should in order to be knowledgeable of my own tradition--apart from a few weeks spent translating the New Testament from Greek back in college.

I don't have a recommendation for a whole Bible translation, but I can't recommend Robert Alter's books enough: The Five Books of Moses and The David Story. Unfortunately, those are the only portions of the Bible he's covered. He comes from a literary perspective rather than a religious one, and has helpful footnotes like "The Hebrew is elliptical here; it could mean A or B."

I also recommend The Prostitute in the Family Tree by Douglas Adams (not the Hitchhiker's Guide guy, but some other very funny guy). Again, not so much is covered, but what's there is gold. It's about the humor in the Bible, including the idea that Jesus was a prankster with some of his miracles.