"The Bible" isn't really one book, and trying to read it as one is ... messy and hard.
It's a convenient collection of a whole bunch of short books.
I'd think reading individual books would be a better approach.
Story books: (written as narrative, can pretty much be read as is, just with lots of historical context need for some "wtf?" And "why is that a good thing?" Moments) Ruth, Esther, Jonah, possibly Mark and Acts.
poetic stories: ( narrative content, but expressed in Hebrew poems, so form and patterns etc more than just reading for the story) parts of Genesis, Job, parts of John, and Revelation.
History (biased, but still intended to be read as history, contains lots of individual short stories): Parts of Genesis, Exodus, Joshua, Judges, The Samuels, Kings and chronicles collection, some of the prophets, Luke, Acts...
"Wisdom literature" / poetry: Psalms, Proverbs, Ecclesiastes, song of Solomon...
And a whole bunch of prophecy, laws, other stories, collected letters to people, and a whole bucket of misc.
Genesis & exodus, as a "ancient Israel primary establishing narrative" maybe a good start if you want to read a whole bunch of the Bible. But then skip and read some stories from later on in Jewish history, try reading some of the more famous Psalms, perhaps with some of the commentaries about them, to see what people believe the meanings behind them are, etc. Checking out some "Bible history timelines" may be helpful too, to get a grasp of when and why different bits were written, and to whom.
Reading about Jesus' life, the four gospels basically cover the same stuff, but written to different audiences, with slightly different emphasis (writing to Jews who knew their religious history, compared to writing to non-Jews living in Roman context who were still investigating this new thing, etc). John is kinda poetic, Mark is all about the action, Luke is trying to be methodical, and Matthew brings in a lot of expected past knowledge of things)... Reading them and comparing them can be interesting to see the different perspectives, but any one of them is enough to get the basic idea.
After Jesus, Acts gives the continued story, what the early church did. And then most after that is letters addressing specific people and circumstances. Reading them as "blanket rules for all ages" without knowing who and why they were written, knowing about the context, what was already the culture at the time, etc, makes them really easy to misread parts as endorsing things our culture does differently, compared to critiquing the situation at the time... I guess that's true of all ancient literature.