This is something I always wondered.
Andy showed he knew the bible pretty well by reciting the book, chapter, and verse of the warden's favorite passage, so it begs the question - was Andy a man of faith who used the bible for more than hiding his rock hammer or did he learn the passages in order to justify himself having a bible in his cell or perhaps to impress the warden?
Does the book cover this?
I haven't read the book - but one knows the film quite well. My take:
A combination of everything you mentioned. I'd add simply passing the time (as to how he came to learn the Bible so well).
Andy was smart and obviously resourceful. He'd have figured out knowing the bible well would curry favor with the warden. Plus it wouldn't have taken him long to figure it could be useful in terms of hiding his hammer.
As to whether the words of the Bible meant anything to him personally - I'd say yes. He'd be awful bitter at humanity (wrongfully accused of murder). It makes sense he would leap to something else to believe in.