Since I find value in a variety of faiths and religions, I've decided to read some ancient texts, one such text being the Bible (again).
Point one: you're looking for 'value' in 'faiths and religions'.
When I've read it in the past, I was a practicing Christian, so I wonder if it's possible to read the Bible objectively and still be moved to believing that it holds truths for our lives?
Point two: 'moved to believing that it holds truths for our lives'.
A search for 'truths for our lives' is, I'd have thought, a different kind of project to reading the bible objectively.
To read the bible objectively is to find out who wrote what, what they literally said,
and why they said it. A lot of the Tanakh is about folk history and folktale, a lot is about the politics of particular times and situations, a fair bit is poetry, and Job is a short story. Then there are books of rules and genealogies and so on. So many authors, eras, angles, stories, purposes.
If you were being objective about the NT, you'd read it in chronological order ─ Paul first (1 Thes, Philippians, Philemon, 1 Cor, Galatians, 2 Cor, Romans), then Mark, then Matthew and Luke, then John. You'd skip 2 Thess, Hebrews, 2 Tim, Colossians, Ephesians, Titus and 1 Tim as forgeries (the polite word is 'pseudepigraphs') or likely so. And Acts is a late weird add-on.
Doing that would give you the history of basic ideas in early Christianity (and bring you to the question, was there in fact an historical Jesus, about whom no one in the NT knows anything, so that his earthly biography has to be told as a concoction of fulfillment of prophecy tales, sayings, and bits?)
But it doesn't sound to me as if that's what you're looking for.
So if you're after 'value' and 'truths for our lives', just read as your instinct takes you and let 'objectivity' look after itself.