You can get various cables to hook up the Gamecube for various video connections.
It comes with a composite video connector. You can go just about anywhere and get the S-Video equipped cable. If you go to Nintendo's website you can buy a Component video equipped cable. And if you really, really want to go all out there's a digital video cable available in Japan (DFP?) that can be hooked up to a VGA transcoder for use with a VGA input or computer monitor.
But it should be noted that 2 channel analog audio is the only thing you can get out of a Gamecube. Yes, most games are mixed for Dolby Pro Logic II. I'd bet that your JVC receiver has PL II decoding. So while the Gamecube won't actually output a 5.1 signal, the PL II decoding of the signal will make it sound reall, really close to 5.1.
And yes, I am aware of the Panasonic Gamecube. Yes, it does actually have a coaxial digital out. But unfortunately that output isn't active during any gameplay, it's only for the DVD output when you're watching movies.