In most cases the hardware does not need or use the extra speed provided by higher-end SD cards, but the Wii may be an exception and there have been no official specs released in that regard. In addition, I read a rumor some time ago that Nintendo plans on releasing their own high-capacity cards specifically for the Wii. I'm not sure if that has since been confirmed or rebuffed, but given the uncertainty at this point I'd wait until you get your Wii to make the final decision.
P.S. The manufacturer of the card has some importance as it may tell you how reliable the product is, but aside from that the name on the packaging makes no difference.
I am waiting to pick up my Wii, however now I need an SD card. I originally thought that all SD cards were the same. However, I found prices seem to range within the same storage capacity depending on the manufacturer and the speed. Does the Wii need a fast SD card? Does the manufacturer make a difference?