Time Machine question

You'll need to login to itunes to enable your music to be played on that computer. (just for the older itunes purchases that still have DRM)

But other than that, it should be fine. The easiest way to transfer them is to backup all of the itunes folders from one mac and "restore" them into the other macs itunes folder. Then you won't have to click and drag for hundreds of songs.

 

I agree about copying all the iTunes folders. Not only do you not want to drag individual artist folders, but you want to make sure you get your Library files so you don't have to add all that music to iTunes on your work computer.