Restoring a Time Machine backup on a new computer with less storage.

My previous computer with a 3 TB drive died. I've a very large music library, over 1TB and my new computer has 512GB so I want to put my music library on an external drive. How do I go about this? I can't look into Time Machine without using Migration Assistant first, correct? If I do that how do I specify for it not to move my music files. And then, will I be able to go into Time Machine to retrieve my music files and transfer them to the 2nd external drive?

Thanks! I haven't found an answer for this yet and I'm afraid of losing my files.