For a classic wedding song, consider choosing "Can't Help Falling in Love," by Elvis Presley. Lyrics like "Some things are meant to be" make this a great first dance wedding song. The classic love ballad, "At Last," by Etta James would also be a very fitting first dance song.
There is a vast selection of songs that are appropriate for the first dance at a wedding, such as "A Thousand Years," by Christina Perri. This song was in the original Twilight: Breaking Dawn soundtrack. An excellent R&B song choice for a first dance is "If I Ain't Got You," by Alicia Keys and Usher. Both of these songs are romantic and talk about the importance of lasting love.