Hi thelnukus,

Welcome to the Support Communities!

I would suggest you follow the steps below to move your music to an external drive.

Make sure you have your computer backed up to Time Machine before doing this.

Click on the link below to see the step-by-step directions you are seeking with screenshots. 

I've quoted some helpful highlights for you:

iTunes for Mac: Moving your iTunes Media folder

If your hard drive is nearly full after loading all your music and other media into iTunes, or if you just want to move all those music and media files to another hard drive on your system, here's a way to make the move while retaining all your playlists, ratings, and play history.

First make sure that the "Keep iTunes Media folder organized" option is selected in iTunes Preferences:

1. From the iTunes menu, choose Preferences.
2. In the resulting window, click the Advanced button.
3. Select the "Keep iTunes Media folder organized" checkbox.
4. Click OK.

Once you've done that, follow the next set of steps to change your iTunes Media folder location to the new drive and then consolidate your library to the new location. This not only copies your audio and media files over, it also retains your ratings and playlists. Note: If you move your music and media to an external hard drive, you will need to have that drive connected to access your files. No matter what, it's always a good idea to have a backup of the media you have in iTunes.

1. Open iTunes.
2. From the iTunes menu, choose Preferences.
3. Click the Advanced button in the Preferences window.
4. Click the Change button in the iTunes Media folder location pane.
5. In the Change Media Folder Location window that appears, navigate to the location where you would like your new iTunes Media folder to be created.
   
   • Note: By default, your iTunes Media folder is a folder named "iTunes Media" in ~/Music/iTunes/ where the tilde "~" represents your home directory.
6. Click the New Folder button in the Change Media Folder Location window.
7. In the New Folder window that appears, enter the name of the new iTunes Media folder.
8. Click Create.
9. Click Choose in the Change Media Folder Location window.
10. Click OK in the Advanced window.
11. From the File menu, choose Library and then Organize Library if using iTunes 9 or later. If you're using iTunes 7 or iTunes 8 for Mac, choose File > Library and then Consolidate Library.
    
12. In the Organize Library (or Consolidate Library) window, select Consolidate files.
13. Click OK.  Important: This action copies all of your music and media files to the new location. There must be enough hard disk space available to copy all of your music and media files.
14. After the folder has been copied, locate your original iTunes Media folder, and drag it to the Trash. Important: Don't remove the iTunes Library files that may be in the same location as the iTunes Media folder. For more information about the iTunes Library files, see this article.
15. Quit iTunes and then open iTunes once more.
    • If you receive the alert "The folder containing "iTunes Library" cannot be found, and is required. Please choose or create a new iTunes library," you most likely moved the iTunes Library files. If this is the case, move them out of the Trash and back to where they were.
    • If you can open and close iTunes without encountering the above alert, empty the Trash.

I hope this information helps ....

Have a great day!

- Judy

You are welcome, thelnukus,

Thanks for reaching out to the Support Communities!

Come back if you have any other questions ....

- Judy

Hi thelnkukus,

The link below should answer all of your iTunes questions:

Apple - Support - iTunes

Regarding backup - I would suggest you use Time Machine to backup your Mac Mini to one dedicated external drive before making any changes.

Mac Basics: Time Machine

Time Machine is the built-in backup that works with your Mac and an external drive (sold separately) or AirPort Time Capsule. Connect the drive, tell Time Machine to use it, and relax. Time Machine automatically backs up your entire Mac, including system files, applications, accounts, preferences, email messages, music, photos, movies, and documents.

Time Machine keeps hourly backups for the past 24 hours, daily backups for the past month, and weekly backups until your backup drive is full.

With Time Machine you can go "back in time" to restore files, versions of files, or your entire system.

If you decide to move your iTunes library to an external drive, I would suggest you get a second dedicated drive for your media.

As a general rule of thumb, you should always have two copies of your important data.

iCloud is not a storage service.  I would suggest using two external drives.

- Cheers,

Judy

Hi thelnukus,

You are correct in thinking that you can also backup your computer to a cloud storage service. 

You can do a search on the internet and find several companies that provide that service, including Dropbox.

Another strategy is to put one of your external drives in your safety deposit box at the bank.

The data and creative projects we create with our computers and iOS devices is precious, I agree.

I personally use all 3 strategies to secure mine.

Cheers,

Judy