I started rereading the Bible last month because I was asked by a student sectarian group about cosmology and black holes. Since I knew that this group believed that the Bible was inerrant (that the Bible was the last word on all issues, moral and scientific), I decided to prepare by reading the Bible again so that I could better defend myself from the onslaught if it came.
And so I bought new copies of the Bible, with extensive annotation, so that I could point out the disagreements between biblical scholars. An advantage of the annotation is how it shows that inerrancy is indefensible, since a careful reading (the annotations themselves will sometimes point out contentious passages!) will show that parts of the Bible do not even agree with each other!
The sources I use, aside from the various Bible translations I own, include the 1611 and 1769 King James Versions, as well as various commentaries. I would have wanted a copy of the Jerome commentary (I first read selections while I was in high school), but was unable to obtain one. I was able to obtain the Oxford Bible Commentary, and I've been using it, as well as the annotations in the various Bibles I own, to see how various traditions (Catholic, Orthodox, Anglican, Lutheran, Evangelical, etc.) interpreted the Bible.
Th nice thing about having internet access is the ease with which you can look for additional sources. So I've also read the wikipedia entries and tracked down the cited references. I'm slogging through the literature, and I find it enjoyable seeing how the various views of scripture evolved.
Among the books I've discovered is Wellhausen's Prolegomena to the History of Israel. (Wellhausen's book --an English translation; the original is in German-- is available in Project Gutenberg.) I'm making my way through it because it provides reasons for why modern Biblical scholars view the Pentateuch as a composite work. Incidentally, it provides a good explanation for discrepancies within the Bible (why the genealogies do not match, why there are two creation accounts, why there are two accounts of Noah's entry into the ark, etc.) --- of course they shouldn't match, since the various sources evolved separately!
The idea of many authors is actually not original to Wellhausen; his main contribution was to synthesize the various hypotheses concerning the sources of the Pentateuch and provide a coherent whole; an explanation that eventually dominated 20th century biblical scholarship. Although there was much resistance from the traditionalists, it eventually became the standard explanation for the origin of the Pentateuch, so much so that the Wellhausen account is now taught in many seminaries and is included in the commentaries to the Pentateuch in Catholic Bibles, and some Protestant bibles as well.
One worrisome aspect of Biblical reading is its inexhaustibility. I've looked at the bibliographies used by the commentaries, and the references grow at an exponential rate. Aside from modern works, there are also many works by ancient scholars (for example, Philo of Alexandria, the historian Josephus) that would be good to read for a deeper understanding of the various religions that emerged from the Mosaic tradition. I expect that I'll never be an expert on it (I'm a physicist, not a biblical scholar!); I will, however, continue my reading for entertainment during weekends.