As a network guy, I highly suggest you don't broadcast the SSID. Manually configure the SSID on your Wii. If you don't want to buy a home router/firewall (which I suggest you do), then you'll be better off manually configuring the Wii's IP, Subnet Mask, Gateway, and DNS.
I do however ALWAYS suggest spending the 20-50us to buy a Wired/Wireless home router/firewall. I prefer Linksys units or Dlinks. They're easy to configure for secure access. That way only the wireless devices YOU CHOOSE will have access. No chance of someone piggybacking on your service.
If you go that route, let me know. I have a word doc with pictures I give to my clients/students when they want step-by-step directions for securing their wireless router. Adding info for the Wii will be a piece of cake.