Funny thing is, I have "theme" songs for each of my kids. Other than my daughter's, I can't tell you how I chose them.
Our daughter's song is "A Whole New World" which was playing in the nursery at the hospital right after she was born. Hubby chose that one since I was still being stitched back up.
https://www.youtube.com/watch?v=hZ1Rb9hC4JY
Our older son's song is this medley of "Over The Rainbow" & "What A Wonderful World" Medley by Israel "IZ" Kamakawiwoʻole
https://youtu.be/Z26BvHOD_sg
Our youngest son's song is "Close to You" by The Carpenters
https://youtu.be/6inwzOooXRU