I like On the Reliability of the Old Testament by Kenneth Kitchen, he is a Protestant, but his take on the Old Testament is very refreshing compare to most modern scholarship. He is a very respected Egyptologist and perhaps the foremost person on the New Kingdom period. And much of his theories are sound in the archaeological record of the ancient near east. Also, he is pretty readable compared to many other books out there.
I have been trying to read On the Reliability of the New Testament by Craig Blomberg, another Protestant, it is a little too scholarly in my opinion, but there is a lot of good information.
If you want a Catholic approach, you can read Fr. Raymond Brown is really the foremost Biblical scholar in the American Church, now I avoid reading most of his OT commentary, but he does generally do a good job with the Gospels and stay Orthodox there. Unfortunately right now, there is a dearth of scholarly interest among Catholics clerics and laypeople writing about the reliability of the Biblical texts, typically the Church does follow modern scholarship in terms of the books were developed.
Now, I mentioned Kitchen above, if you want you can read his archnemesis David Rohl, who wants to prove the Bible right by redoing the entire chronology of the ancient near east by 250 years, for instance he wants to identify Sheshonq with Ramses II rather than Shishak. And he wants to make David and Saul contemporary with King Tut and Akenaten.