Reddit mentions of Holy Fable: The Old Testament Undistorted by Faith

Aside from Finklestein's book, there is Robert Price's Holy Fable: The Old Testament Unencumbered by Faith. Robert Price is a former evangelical minister-turned-atheist, but with a deep understanding of the bible. It is maybe a bit too skeptical, but it's still got a lot of good info.

In general:

The Torah / Pentateuch was written by (at least) 4 different sources, and compiled (much?) later. There's the Elohist, the Yahweist, the Deutoronomist, and the Priestly source. This explains why there are 2 different versions of a number of stories - for example, there are 2 creation stories; Noah is simultaneously the "only righteous man" God could find, and also a lazy drunk; there are two full sets of 10 commandments, only 3 of which overlap (so there are actually 17 commandments) etc. Someone (likely the Deutoronomist) compiled the book, and not wanting to risk being wrong, included multiple stories and tried to make them jive with one another.

Generally speaking, Moses is nearly universally agreed to have been a myth, along with Joshua. There is no archeological evidence that ancient Hebrews were ever in Egypt, or ever wandered in the desert for 40 years, although stories of Pharaoh may have come from a time when Egypt ruled the Levant (Moses is an Egyptian name, from the same root as Tutmose or Ramses).

The ancient Hebrews were, most evidence supports now, one of many Canaanite tribes, and happened to be the one that managed to stick around. They were also polytheistic for a very long time into their existence - a number of stories have been altered to whitewash this out. The 12 (13? 11 plus grandsons? sources are all over the place on this one) sons of Judah/Israel heading the 12 tribes of Israel are likely figureheads that were ret-conned into existence as more tribes joined with the Hebrews through conquest. Kind of like "Oh, well, we'll join you, we're probably related somewhere way back anyway!". There is also little to no evidence of an epic conquest of the holy land, a. la. Joshua, and many of the vast cities and huge fortresses referenced in the book of Joshua were, archaeology says, minor hamlets with hundreds or thousands of people at most.

There is very little evidence for the existence of David. There is an inscription on a very old (non-Israelite) stone tablet that may reference the "House of David" from several hundred years after David was supposed to have been around. I'm willing to concede that he may have existed, but he was likely a "chieftain" rather than a king. Almost all scholars agree that there was never a united kingdom of Israel and Judah. Jerusalem, at the time of David (10th century BCE), was a very small village or outpost, and there is also no evidence of a first (or Solomon's) temple. There is, however, ample evidence of a 2nd temple (which was greatly expanded by Herod near the BCE/CE switch).

1,2 Kings was written either during the Babylonian exile, or shortly after it. There are just too many anachronisms (bronze weapons, camels, etc) for it to have been written during the time of its subjects, and its subject matter (continued allegiance to Yahweh will bring you victory, breaking Yahweh's commandments will bring you strife) is clearly aimed at explaining circumstances to an Israelite population that has experienced lots of strife.*

1,2 Chronicles, Ezra, Nehemiah (originally all one work) looks to be a redaction and rewrite of 1,2 Kings in large part, but by the priestly source - who is working hard to clean up the image of certain people (David had Uriah killed? Nah, let's skip that. David's sons did bad things? Nix it. etc) at the same time that he's working to ret-con a place of prominence for priests of his tribe.

Anyway, skipping ahead to the New Testament, I would also recommend another extreme skeptic's book: Dr. Richard Carrier's On the Historicity of Jesus. Dr. Carrier's position is well outside the mainstream consensus, but there's no denying that A.) He is extremely well versed in his subject area, and B.) the mainstream consensus is very conservative, as it is made up of largely religious institutions and believers who all have a vested interest. So his book is good for contrast, and the truth is likely somewhere in the middle.

For starters, the earliest parts of the New Testament are the letters of Paul. Paul, for sure, wrote 1 Corinthians, 2 Corinthians, Galatians, Philippians, Philemon, and Romans 1-8. The rest are kind of up for grabs, with some possibly by Paul, and some certainly being forgeries and written as late as the 2nd or possibly even 3rd century. Paul's Jesus is very vague (as in, celestial, not earthly, and working through revelation), and Paul nearly goes out of his way to not talk about Jesus' earthly life - even in places where Jesus ostensibly talked about specific topics that would indisputably bolster Paul's arguments.

Next, we have Mark. Mark's gospel was written first, and Mark's Jesus is somewhat timid and understated. Mark also has little understanding of Galilean geography (the vast "Sea of Galilee" that witnesses such horrible storms is, in reality, a pond that you could kayak across in an hour, for example). Then, Matthew wrote his gospel, using Mark as a source, along with possibly the "Q" source, or possibly just adding things that he had heard or liked. Matthew's Jesus is a scholarly rabbi, and he talks of how Christians should keep the Jewish customs along with the new customs of Christ. Matthew also corrects Mark - a lot. Then, we have Luke, who uses Mark and possibly "Q" or possibly Matthew as his source. Luke's Jesus is the Gentile Jesus, who brings new rules and is for everyone, not just Jews. Those are the Synoptic gospels; then we get to John.

Oh, boy. John... is nuts. John's Jesus is large, in charge, and slinging miracles and witticisms in every direction. There's nothing about helping the poor or healing the sick, but there's a huge serving of hating the Jews. John also contains a number of Gnostic themes that have likely been toned down over the years - John's gospel is the one that is most obviously cut up and rearranged and altered. There's a lot of things like "And then Jesus did his first miracle. And then he did many other miracles. And then he did his second miracle", or Jesus teleporting, popping up all over Galilee, one place after another. But anyway, it’s likely that John’s gospel was so popular that it couldn’t be kept out of the New Testament, once the Council of Nicaea got around to picking which books got in, so it had to be altered in order to tone it down a bit.

The contents of Acts are impossible to square with the letters of Paul - Acts tells a story of the early church, huddled together, building outward, ministering to Galilee, growing larger in harmony. But Paul - Paul does not get along with the so-called fathers of the church in Jerusalem. We also know, partly from other sources, that the early church was very fractured, and only now looks harmonious because the winning faction got to poke and rewrite a lot of the history.

The rest of the New Testament was largely written in the 2nd and 3rd centuries, and can't have any relevant information to share about the life and times of Jesus, having been written several generations at least after the last person that could have ever met him had died.

Anyway, that's a more-or-less short version of some of the ins-and-outs of some major episodes of the Bible.

* Totally my aside: the concept of religious guilt, IMO, stems from here. In olden times, gods were like mascots - you moved to a new place, you adopt the local gods -
or, you get conquered, it must have been that their god was stronger, so why not jump on the winning bandwagon. The Deutoronomist, the likely source of the idea of the "covenant with god", introduces the idea that believing in a god is a two-way street. Believe enough, and do what he wants, and good things will happen -- but don't believe, or don't do what he wants, and now bad things happen, and it's kinda your fault. The aim was to keep the Hebrews from converting to Babylonian or other Canaanite gods.
Cue thousands of years of catholic guilt, etc.

To increase your intellectual enjoyment, I recommend Robert M. Price's Holy Fable: The Old Testament Undistorted by Faith. It's a chapter-by-chapter commentary giving (skeptical) background and historical insights. You can keep that open in your Kindle and the Bible open in another window (I recommend the Blue Letter Bible for online reference), and go back and forth between them.