You can get a wireless router at Best Buy for $50-75. You can find ones cheaper than $50, if you look. You should get a router with the new 802.11n wireless standard for future wi-fi devices you will buy. Wii uses the older/current 802.11g standard, but any 802.11n router will also do older standards like 802.11g/802.11b.
To answer the question about having a PC in the same room as the Wii, then answer NO. The wireless router can be anywhere in the house (within 50 or so). The router connects directly to the DSL modem that the cable/phone company gave you. Then you can hook up multiple devices up to the router (like PCs, Wii, Blackberry, etc), either wirelessly or via ethernet cable, to share the internet connection.
For me, my router is an Apple Airport Extreme (works with both Macs and PCs). I connect my iMac, Wii, and Nintendo DS to the router wirelessly. I also connect, via ethernet cable, my older Windows PC, Dish Network Receiver, and other rooms in my house (my house is wired with ethernet/network cabling). All the rooms that have cable, phone and ethernet jacks run to a centralized distribution center in the basement. My router (as well as cable modem) is at the distribution center where the cable/phone enters the house from the street.