I have an Imac G5 with no Airport card installed but want to listen to music from the internet on my stereo in another room. Just to make sure, is this what I need: an Airport Extreme card and an Airport Extreme base Station? I already have a wireless dsl gateway (router) from my ISP. Could I use that instead of the Airport Extreme card?

You need an Airport Extreme card for the iMac and an Airport Express as show on this page http://www.apple.com/ca/airportexpress/

I doubt you can use the wireless router, although I'm not sure.