for the wii menu, you need to upgrade to 4.0 for it to work.(use the nus downloader for the 4.0u wad and install that, don't upgrade to 4.2 as it can brick your wii(even if official). I'm not sure about 4.3 though.
Hi,
As far as I am aware the Wii in its unmodified state will only support SD cards (not SDHC) up to 2GB.
However, there are programs for the Homebrew Channel which support SDHC, e.g. media players.