Answer
This question was answered on April 16, 2006.
Much of the information contained herein may have changed since posting.
This is a multipronged question so I will answer each question seperately.
1. Will the router need to be hardwired to the desktop? In one word, yes. Here's how the connection would need to be: The cable line goes into the cable modem, from the cable modem, you will need to run an ethernet line to the router. From the router another ethernet connection will be needed to the desktop. This is necessary because the router will not accept a regular phone line cable. Besides, you're paying the money for the higher speed, you should take advantage of the speed and an ethernet cable will help make that possible.
2. An ethernet card is relatively easy to set up and best of all, they are really really cheap. An ethernet card shouldn't run more than 20 dollars. If you don't feel comfortable installing hardware, you may want to seek help with the installation from a professional.
3. You didn't ask but since I just set up the Tivo to the wireless router last night, I went through a 20 minute growing pain I'd like to help you avoid. You'll want to review Tivo's website for instructions on how to set up the network. It's easy to do, but if you're new to networks, there will be somethings their tutorial will teach you. Here's the website: http://customersupport.tivo.com/knowbase/root/public/tv2013.htm? Once you get this up and running, you'll be really glad you did.