Build a music player for WP

Hello, How are you today? We need to create player for a werdpress website. Player Features: 1) Play continuously, not stop or pause upon page away navigation 2) Float on bottom right corner of screen 3) User should be able click on the big thumbs in the home page and player starts playing, similar to [login to view URL] 4) Modern design 5) Play, stop, pause, next, shuffle, etc buttons 6) Play mp3 music from a wordpress custom post type "Music" 7) Work in all platforms windows, mac, iphone, ipad, android, tablets 8) Responsive Do you know any plugin we can use as a starting point? Should we build one from scratch? Website: critic . fm More than 30$ is good! Thank you!