I don't have a favorite, but in general I like the opening music and menu music in GT1 the most. The opening music (a Chemical Brothers remake, I think) is my favorite of the series to this day. And the menu music, with somebody jamming out on a guitar, nothing special, just some band jamming out, by far gets me the most pumped for racing!
I don't know what happened in later GTs, so far as menu music goes. GT2 has that super-quick jazzy stuff which gets on my nerves. Good thing I could turn this off. GT4 has music which sounds like it'd be fit for a funeral dirge or something. Bleagh. Depressing. Like I'm in a doctor's office waiting to hear if I'm about to spend the next precious years of my life taking suppositories or something.
Later GTs, of course, we could substitute our own music. But I do like some of GT5's default jazz and ambient selections.
As I'm racing, I don't have music on, ever (except in GT5/6 in which I can add my own), so I have no idea which tunes are in GT1. I just had a listen to Feeder's Sweet 16 though. Yeah that rawks! ... It'd be too distracting for me though as I'm driving.