The other hookup method I can see, and may prefer, is through a wireless network. I don't currently have one, but I'm certain I will as soon as I can afford it after the move, simply to eliminate the need to cut a lot of holes into the plaster walls to run Cat5 or any other cabling. I understand basic wireless networking - however, how would you hook up a Rio Reciever? There's no place for a PCI or PCMCIA card... How would that work?

I recommend going the wireless way, being a wireless engineer myself. To make the Rio Receiver wireless you would get a wireless ethernet bridge here's one from Linksys WET11. or this one from D-Link DWL-810+ I prefer the Linksys one as it has a higher transmitter power and larger gain antenna.
You just connect the wireless bridge to the ethernet port of the Rio receiver, no drivers, you can configure it with your web browser. Then all you get is a wireless access point connect it to your hub or computer. Instead of an access point you can get a wireless PCI card for your PC and connect it to the wireless bridge in Ad-Hoc mode, but an access point is better.

cheers,
Jai