I listen to internet radio all the time on my computer. Tomorrow, I believe, a certain jolly old elf is going to leave an internet radio at my house. I'll let you know if it works as advertised.

If your cable modem does not already have a wireless access point, you will need to add a wireless access point to your router. It attaches with a single cable and should not be a problem to install although you may have to do some minor fiddling around with settings. You could also probably take your current modem back to your cable provider and swap it for a modem that already has wireless access.

Yep, easy to use. I got a Tangent Quattro. I opened the box, plugged it in, and found first my network and then my favorite international station in less than 60 seconds. I've been happily exploring world news and poking around for classical and jazz stations. Right now I have WBEZ from Chicago playing and before that I was listening to the news from France on RFI. Amusingly, my favorite local station is not available, but I've already requested that its stream be added.

Another option for you would be a Logitech Squeezebox, but that needs to be played through a receiver.