You could however, upload them to a 3rd party site such as dropbox or something, and create a website that links to those links. Keep in mind that you will need to have more than just links to the downloads on the website. Perhaps a place to comment, rate, discuss, etc. the midi files or something related to the midi files. Also, I'm pretty sure that even if you upload them to dropbox, if they are copyrighted by someone and you do not have a license to distribute them, then you will still be banned for copyright infringement. If they are your own files you should be fine though.
EDIT: Reread the first post and have a few tips:
For the uploading of users files, make them use an external host (like dropbox) and require them to accept a content agreement that gives you a license that let's you distribute the files (at the very least.) I am fairly sure that the discussion would qualify as a website, and I am not sure what cms you should use, as I do nearly everything from scratch.