There are a huge number of songs included in the Wii U version, and you can adjust how often a song plays by going into My Music.
You can freely adjust the settings so all songs have an equal chance of playing or make it so only one song plays.
In My Music, you can adjust the song settings not only for the stages, but for the menu screen as well.
The songs are not all available at the start of the game. Find CD items in the game to expand your collection. CDs can appear during matches or as rewards in Challenges.
Most of the songs from the Nintendo 3DS version are available in the Wii U version. There are also songs from past titles and new songs too. You can see the list of musicians and their songs via the following link: