...honestly F-Zero GX has some great tunes.

Bio Rex's is some pretty good thrash metal I think?
Phoenix (despite being a cop) has a pretty good rock number
Captain Falcon's is ... well it's ... it's very Captain Falcon. That's... all I can say about it honestly. I love it but... wow.
Leon's theme is an instrumental track and it just friggin rocks. It's my favourite.
Pico's theme is pretty great too for some synthy, bassy, electronic music.
Then there's Silver Neelson which is full on cowboy.