
Most of the Old Testament consists of Jewish history, beginning with creation. There are a few that could probably stand on their own: Job, Jonah, the Song of Solomon, Proverbs, and maybe Psalms. (You would miss a lot in Psalms doing this.)
The New Testament is full of allusions to the old and cannot be understood correctly without reading it first. It probably doesn’t matter the order you read the first four books, or even if you read all four - Matthew, Mark, and Luke are very similar in tome and they describe the same events, but you wouldn’t want to skip John.
Acts is simply what happens after the four gospels, and the remainder of the Bible consists of epistles from the apostles which refer to events in Acts and in the gospels, and it wraps up with Revelations.
I don’t really see how you could read it in any substantially different order and get as much out of it.
