When I still had my HP desktop, we used the WiFi USB connector to hook up to the internet wireless. It is now discontinued, and for good reason. It was very buggy. When it worked, it worked great. Basically set up your desk top as a wireless router and used your existing internet connection through the computer.
Now, with my iMAC, I just share the internet with the built in WiFi and connect through there. No additional hardware required, all built right in. There is a hardline LAN input on the back of the Wii, which would be the easiest, but if you have a LAN, then use the wireless. Works like a charm.