Generally Apple just puts it on the root level of the hard drive... but there isn't a limit or set spot. I put my Mac OS 9 system folder in a folder called Mac OS 9 in my Applications folder.
And yes, if you need Mac OS 9 for Classic, then moving it over will work. You just need to point Classic (via the Classic Preference) at the system folder once moved to your hard drive. the first time it goes to run it'll add any software it needs to the system folder and you should be ready to go after that.