So after dropping out of school, I have the option of keeping the laptop should I so desire. However, to do so is 1500 bucks, and I can get a better one for less, so fuck that, I'm gonna return it. However, I do need to take a lot of files from it (mostly music), several gigabytes worth. What would be the quickest and preferably cheapest way to do so?

Put them on a thumb drive and compress them.

Put them into files, compress them, or zip them. Either put them on a flash drive or onto a CD-R, put them on the new computer, unzip folder, and you are good.