If all you did was install HBC, then you're not fully modded yet.
Check out the Softmod Any Wii guide (link in my signature) and follow it completely. It will include collecting a backup of the system's NAND memory as you mentioned.
SD cards may not be the best way to go due to the read speed compared to USB, but the loaders may be configured to read from SD. I've never tried it. But if you go through the entire guide I mentioned, it ends with giving you an app pack to start things off with which will include three USB Loaders. Each loader has the capability to rip game disks and store the data on USB for non-disk playing in the future. You'll have to check the settings for each loader to see if it can be saved to SD, but as I said, USB is preferred over SD due to the read-write speed difference.