The normal place for Music files on a Mac is in the your user's Music directory. That's right at the top level of your home directory. There are several directories there that are "important" on a Mac:
Documents
Downloads
Movies
Music
Pictures
As you indicated, there's an ITunes directory under Music. Which makes sense because ITunes puts it's music in the Music directory, but it makes its own directory so it will be obvious that those files are "owned" by ITunes.
I have several directories under Music like:
FLAC
MP3
downloaded_from
The first two I made back when I had quite a few MP3s and was ripping all of my CDs to FLAC. Now I have maybe 4 or 5 albums in my MP3 directory and quite a few in my FLAC directory. "downloaded_from" is my way of keeping track of where I got downloaded music. For example, when I buy something from Bandcamp, I put it in the downloaded_from/bandcamp/<artist name>/<album name> directory. That way I know where it came from if I need to know later.
When you run MC for the very first time it tries to find your music. I'm not sure where it looks, but the Music directory is probably in it's list of places to search.
But even if it doesn't look there, you can easily configure MC to find your music no matter where it is:
Tools > Options > Library & Folders > configure auto import > Folders > Add
Using that dialog you can add folders to be monitored for new music. That way MC finds it automatically when you add music in any of your "auto import" folders.
I hope this helps clarify things and points you in the right direction.
Brian.