If you want something reliable, dependable, and safe to store your Wii backups on?
Don't buy a flash drive. Plain and simple. They cause issues in Nintendont, the Wii sometimes just corrupts them, sometimes completely kills them. This is because of the several read-write cycles that the Wii does to the drive when playing a game from it. Hard drives do not have this issue. They're faster, more reliable, and have a lot more storage per dollar.
Flash drives are not good in the aspect that they don't hold up very well to extreme usage that happens when playing a Wii game from them. They will die faster than a hard drive.
Hard drives don't always have to be huge and ugly. You can tuck it behind the console, under the cabinet, inside a cupboard, whatever you've got to do. They've gotten really small in recent years; you can get something like this that is both aesthetically pleasing and very small.