What is the best way to copy my music files over to to a new computer?

Complete instructions are here:

How to move your iTunes library to a new computer - Apple Support

Make sure you create a fresh backup first.

Moving a library: Quick answer if you use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its sub-folders and files) intact to the other drive, hold down the option/alt key (shift on Windows) while starting iTunes, and when requested to select a library select the iTunes Library.itl file in the copied folder.

When this is to a new drive/computer put the copied iTunes folder in the default location of Macintosh HD > Users > *User Name* > Music (or Home > Music) then you don't even need to start with the option key held down, iTunes will automatically look for it there. (Make sure there isn't anything already in the iTunes folder there that you want to keep since you will be replacing it with the one you are moving.) Remember to authorize the computer in iTunes to your Apple ID if you use this to sync to Apple mobile devices or play DRM protected media (e.g., movies).

Certain items used in iTunes related activities are not stored in the iTunes library folder but in special folders. If you are moving a library to a different computer you may wish to copy these too:

- Apple Music cache files: http://dougscripts.com/itunes/2015/09/new-flush-apple-music-cache-files/ - ~/Library/Caches/com.apple.iTunes/SubscriptionPlayCache/ folder, which is sort of like an “iTunes Media” folder for Apple Music

- iOS device backups, various preferences files: https://discussions.apple.com/thread/3285925

Items should be sorted out in major groups in iTunes > Media

Your media folder is not standard. I don't know why but likely you changed some setting in the past.

iTunes: Understanding iTunes Media Organization - Apple Support

Image of folder structure and explanation of different iTunes versions (turingtest2 post) - https://discussions.apple.com/docs/DOC-7392 and making an iTunes library portable.

Right click on a track in iTunes > Show in Finder

Unfortunately there's not much I can do from this end other than suggest where and how to look.

It sounds like you may not have have had iTunes set to organize your media or something happened to mix up the folders in the past. Normally they should be set up in folders as one of the earlier links describes.

It is actually pretty easy. Drag a folder to a drive, drag a folder to another drive. You had a non-standard setup somehow and I know I still don't have it all straight how things were set up (not that it matters now).

your apple content follows your apple ID. no matter the pc or mac it will go to that iTunes program you just have to authorize that iTunes program on the new computer your running and you can download your purchased content to that computer.