Hello and welcome to WiiChat, Robin.
The Wii out the box uses wireless internet. If you have your PC (it doesn't matter what OS it is) running through a wireless router, then your Wii should be able to detect it. The Voyager is your DSL modem, which needs to stay in the loop.
In other words:
-> = connects to
Wall->Voyager->Wireless Router->PC (then your Wii picks up the wireless signal)
A suggested Wireless Router if you don't have one or know what you're looking for:
(though you can get other brands cheaper)