Here is a great article on How to Choose a Wedding Song. It goes covers three steps to choosing your song. The first step is figuring out your style, then consider song criteria and finally looking at wedding song lists. The article explains each step and guides you to figure out how to pick a song. It also provides links to wedding song lists. Besides the three steps the article gives other helpful tips such as choosing two songs or doing audio clips of different songs to tell the story of your relationship. I definitely recommend checking the article out.
Theknot.com also has a bunch of different articles about wedding songs. Such as songs you should not use, romantic first dance songs, first dance cover songs, music tips, music myths, music mistakes, and much more so I recommend looking through there as well.
For my film I do not need a specific first dance song, however I do need a score for the movie. I will have someone compositing the music for me, but I have also been looking around on soundcloud.com to get ideas of how I want the music to be. Here is one of the songs that I found: