back up iTunes library on a USB stick?

You can do this, but don't use the iTunes "backup" option. Instead, just copy your entire iTunes folder to your USB drive. You can rewrite this folder each time you want to backup. (The iTunes folder does have to be smaller than the total memory capacity of the USB drive, but I assume you already know this.)

I only keep my purchased music inside my iTunes folder. All of the music I ripped from CDs is kept in another location on my hard disk--this makes backing up the iTunes folder much easier. (I keep separate backups of my ripped CDs, because I have had problems with these files too and it's not fun to sit hour after hour re-ripping CDs.)

If everything in your iTunes folder fits on an USB drive--it can't hurt to have a backup copy of all your music files.