If music is not showing up correctly it's either badly tagged, you've used a program that fetches data, but does not save it to tags or just keeps it in a database. The third option is that the application you used to use used a special field for tagging, which MC does not pick up. Either way, it should be fairly easy to fix, as long as your directory structure is good.
For both Movies and Music I would create a view and add "File Name (path)" library field. If you sort by this, you'll have your media sorted by video, video types (if you have sub folders here), and then music, artist and albums.
I would start by selecting all videos and change the Media Type to video. Then change each sub type to the correct Media Syb Type. You do this with the Action pane. Choose tagging and select the appropriate fields you want to change. Then I would start with the albums and artists. The compilations might create a mess. In MC, most people use the "Album Artist" field. This would be the name of the compilation, and you can use artist to add different artists to each track.
This was written very fast, but I hope some of this made sense. If you have more trouble, try to ask for one thing at a time, and I'm sure we would be able to help you with the best solution.