You can set the Genre in iTunes, selecting individual tracks, multiple tracks, and/or albums before doing so. To get the best out of iTunes I suggest that you need to stop thinking about files and file names - iTunes gives a very powerful, flexible set of capabilities to manage and organize music based on metadata (some of which is embedded within files, some of which is held in the iTunes "database" file). I've always used the options (under Edit > Preferences > Advanced) to Keep iTunes Media folder organized and Copy files to iTunes media folder ... although I know how iTunes then manages files and folders it really doesn't matter except in cases where I need to resolve minor issues. For example, my iTunes copy of the von Karajan/BPO recording of Beethoven's 5th symphony happens to be stored in this folder:
E:\iTunes\iTunes Media\Music\Berlin Philharmonic Orchestra _ Herbert\Beethoven_ Symphonies Nos. 5 & 8 _ 'Fide
and the 1st Movement is this file:
01 Beethoven_ Symphony #5 In C Minor.m4a
but the important thing is that it appears like this in iTunes, correctly ordered with other Beethoven works:
Key thing for me is to let the metadata determine the folder and file structures and names, not the other way around. In this example works are grouped by the original CD content, but there's no reason why you shouldn't use the Album field to divide this into Symphony No. 5, Symphony No. 8 and the Fidelio overture if you want to keep specific works separate.