I've just finished listening to Faith Comes By Hearing's [also known as bible.is] lightly dramatised King James Version audio Bible. It was very well done, with only a few irritations. The speakers read with meaning and very good pronunciation of Jacobean English and biblical names.

I'm now re-reading The Books of the Bible, which is an innovative and inviting Bible, designed to make it easy for you to read the whole thing. This version removes the chapters and verses [but does use space creatively to show logical sections].
It rearranges The First Testament to be closer to the Hebrew Bible format, re-ordering the Prophets chronologically, and dividing into large sections approximating the Hebrew Bible's Law, Prophets and Writings sections.
If the Bible seems like a book of great stories, interrupted by genealogies, this statement from the article introducing Genesis-Kings (The Covenant History) might make better sense of it:

A simple list of people or places provides a "skeleton" that an inspired author fleshes out by telling the stories of the various people or places on the list. This turns each list into a chronicle that traces the unfolding larger story of God.

The New Testament begins with Luke-Acts and Paul's letters, arranged chronologically [because of Luke's connection with Paul], then Mark and Peter's letters [because of Mark's connection with Peter], Matthew, Hebrews and James [the Jewish-flavoured New Testament writings], and ends with John's Gospel, letters and the Revelation.

If you would like to read the whole Bible, I can't think of a better one to use in your project.
But, if reading is a chore, listening to The Bible Experience, an African American presentation of the NIV, could be a good plan.