You mean wireless router? That's what you need for connecting your wii to the internet, unless you want to use LAN.
I recommend any Linksys router that says on the box 'wi-fi certified'.
You can get them for around £30-50. www.linksys.com - this link will probably be right, I don't know as I have just guessed it lol. You could try searching google though.
Ok, so you want to connect your wii through LAN.
google 'wii LAN adapter' and you should get some results, I connect my wii wirelessly so I don't have any experience in this field of internet connectivity.