Traditionally, the family dances will be a Father-Daughter dance and a Mother-Son dance, and these will typically take place immediately following your first dance. Depending on your family situation, you may or may not follow the traditional format.
There are a lot of fun options for family dances, whether traditional or untraditional. If you are putting a unique spin on your reception, how about a sibling dance, step-parent dance, or grandparent dance? Use your creativity and talk to your wedding planner or music coordinator to discuss ideas.
I put together a playlist of all of the most common songs requested for family dances and have combined it with some of songs from most lists of the popular family dance songs from several reputable sources.
The Knot - https://www.theknot.com/content/classic-first-dance-songs
The Huffington Post - https://www.huffingtonpost.com/entry/most-popular-wedding-first-dance-songs_us_5783f9c5e4b0344d51508125