To play just Wii games from a USB HDD you need to format the HDD to WBSF format using WBSF Manager 3.0 (or some other programme capable of doing so). But WBSF Manager can only format the whole drive (as far as I'm aware.) I know this site says you should format the drive to FAT 32 because then you can run your apps and stuff from the same drive, but Wii games do not run on a FAT 32 partition/drive (at least not when I tried).
I have a Seagate 1TB hard drive too completely formatted to WBSF using WBSF Manager 3.0 and use CFG USB Loader and Wiiflow. I don't use my HDD to play GC games because my copy of Paper Mario: Thousand Year Door is slightly damaged, only Wii games. To run homebrew apps I use a SD card formatted to FAT32, I find it easier for me.