The songs are why you are there.
I am not going to tell you what songs to play, just that you need to be a jack of all trades when it comes to styles. Standards change, crowds are different and you will figure out what the core style is of your band.
There are some things to remember.
Learning Special songs is the mainstay of the wedding musician.
Most of the time these special songs are for the couples first dance or for the parent/child dance. I can not emphasize enough, No mater how you feel about the quality of the song, the artist who sang the song, or anything else - play it the way they want it and sell your performance like it is the best song you have ever heard in your life.
A heads up -- there has been a trend lately for couples to have their first dance choreographed. If the couple has had thier first dance choreographed and if you can not play the version of the tune they want, EXACTLY how they want -- make your strongest recommendation that they provide you the MP3 for their dance and play that on the PA.
It pains me as a musician to say that, but once again -- it isn't about you, it's about them.
Another trend is the "Do not play" list.
I am not quite sure how that got started, but the group I play with has seen do not play lists that initially eliminate 90% of our available catalog.
Typically, the reason for an extensive list is, the bride and/or groom do not want anything that would be considered "cliché", but don't realize there is a difference between cliché, and standard. Not that I haven't played brown-eyed girl 5000 times and would be happy to never play it again, but the crowd loves that song -- you and I are there to entertain the crowd.
With that said, one or two items to not play usually indicates that certain songs might have meaning or memories that the bride/groom don't want brought up at their wedding. If it is a signature tune for you, try and get a good reason, but leave it at "I don't like that song" or "To many memories".
Also, you may get requests that you realize the bride and groom really have never really listened to, or may not be aware that it is in bad taste to play at a wedding.
Scenes from an Italian restaurant, Happy Anniversary, Rose Bouquet, The Humpty Dance are all tunes that people have asked for, "The Humpty Dance" being the only one the group I play has actually done - and only after several rounds of "Are you sure?", and finally performed with a good deal of "Louis Louis" worthy slurs and mispronunciations.
However, one I have never figured out (and we play it too) -- that is consistently in the Top 10 list of requested and performed wedding songs is "Every Breath you Take" by the police.
Have you ever found yourself in a situation where asked to play a turkey of a song, or something that was woefully inappropriate, what did you do?