SDHC should work, but I dunno if any of us have really tested it yet.
To install you need to follow the whiite install instructions, you will need to use fdisk or some other
partitioning tool, no questions about it.
If you need the .dol, you can get it from the gc-linux sourceforge, that will be booting the SECOND partition on your sdcard (/dev/rvlsda2)
Bert's doesn't have a text editor that I know of, but I was going to include one in my Gentoo distro I'll be releasing whenever this horrible compiling stops and I can finally add more applications.
So a quick breakdown, you backup whatever is on your sdcard on your computer and then reformat it. Choose how much space you'd like to allocate to the HBC, that will be your first partition, /rvlsda1, this will need to be a vfat partition.
The rest of the space should be allocated in a second ext3 partition, this is where you will house your xwhiite, you will need to mount /dev/rvlsda2 and then unzip bert's files to that, for the HBC, you'll need to drop in the kernel.dol and those image/xml files if that's yer thing. If you don't know linux or use windows I've heard it suggested to get yerself a ubuntu livecd and use the GParted that's available on that. You can mount ext2/3 in windows with applications but you're much better off doing it in linux and most people willing to help you will most likely have most experience with the linux utilities (fdisk is crazy easy to use once you get it)
Also, by the way, any of you can add applications to whiite or xwhiite just using apt-get. Look up some documentation on that if you want to add to it, really, there isn't much to putting Linux on Wii as the GC-Linux team has already made it so easy for us.