Some have suggested that a good wedding reading is something from the Bible, but not being extremely tied down to the typical traditions and whoopla that go along with any particular church, I think that you can find very meaningful text in many places. Some quite unexpected.
We did not get married in a church or for that matter by anyone that would be considered tied to a mainstream, traditional type church. The person that married us was in fact a woman from some progressive denomination who was introduced to us by a very dear friend and she has spoken at another good friends funeral. So, we knew that since neither of us was tied to anything in particular "God wise" that she would be the one to marry us.
We got hitched in a park next to a waterfall. All those in attendance stood around the balcony of the park walkway. It did not last very .long. The reading that I found came from a book that I really hated, but think that I was meant to find this passage because it was so us, "It's clear to me now that I have been moving towards you and you toward me for a long time. Though neither of us was aware of the other before we met, there was a kind of mindless certainty humming blithely along beneath our ignorance that ensured we would come together. Like two solitary birds flying the great prairies by celestial reckoning, all of these years and lifetimes we have been moving toward one another". I had it put onto parchment paper and it is framed and hangs with a few wedding photos now.
Sometimes when reading the most mundane material, because I just hated the book and the movie, you can find a passage most profound and meaningful.