Most wedding receptions will start with the brand new husband and wife having their first romantic dance as their life together begins.

After the first dance, tradition has two further dances. The first of these is with everyone dancing, but led by the bride and her father with the second again everyone, but led by the groom and his mother.
It's entirely upto you how many songs you have to start your new life together. Some only have one and invite their guests to join them half way through. Others have two and do the first on their own and invite all guests to join in on the second.
The only advice we can offer is to do what you feel is right. Some people hate the thought of dancing infront of their friends and family, other relish it.
One thing we really can help with is the choice of song. Unfortunataly when you listen to most slow songs, they are actually about people breaking up so not very suitable as a first dance! Here are the lyrics to a song that is about people being in love, I'll Always Love You sung by Taylor Dayne, so you can see if the lyrics suit your situation. You can also hear an audio sample and check out some father/bride and mother/groom songs too, all by scrolling down.