There are a few ways you could go here! Two classic introductory texts to the Hebrew Bible are Who Wrote The Bible? by Richard Elliott Friedman and How To Read The Bible by James Kugel. Both are written by professors in the field and discuss the context and history behind the writing of the Hebrew Bible and give an introduction to academic analysis of the Bible. I can personally vouch that How To Read The Bible is a great and compelling introduction. The one issue is that both (especially the Friedman book) talk primarily about the classic documentary hypothesis on the authorship of the Pentateuch (first 5 books of the bible) with no mention of the more modern alternative hypotheses. The documentary hypothesis used to be the consensus model but has fallen apart in the past few decades, although there's no consensus replacement for it. Understanding the classic documentary hypothesis is still essential context to academic biblical criticism though, so you're not wasting your time - just be aware that although parts of it are still relevant, current models complicate things. I've also heard good things about Introduction to the Hebrew Bible by John J Collins.

You might find it helpful to have an annotated study bible - the New Oxford Annotated is the most widely used standard as far as I know and will at least give a broad overview of everything you're interested in. It uses the NRSV translation and includes essays on the history and authorship of the bible, historical context, maps, short essays introducing each book. There's also running commentary in the footer of each page that provides crossreferences and helps with thorny passages.

In terms of archaeology and bible history, The Bible Unearthed by Israel Finkelstein is a well known popular text but it's important to note that it's getting a bit old now and some of his opinions have changed somewhat since - its "minimalist" stance was/is a minority viewpoint too. William Dever's Beyond the Texts is well regarded and by a leading expert in the field although it's pitched at a slightly dryer/more academic level - it's definitely worth checking out if you're interested in the history of ancient Israel/Judah before the exile and it clearly lines up what in the bible is proven, disproven or possible but with limited or no evidence.

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For the New Testament, I'm less familiar with the texts so I can't be too helpful but I know the Bart Ehrman book A Brief Introduction to the New Testament is regularly recommended and widely used on college courses. Hopefully this is somewhat helpful!