Using Copyright Material for Promotional Purposes

I've been thinking a lot about copyright and music publishing lately, and I was wondering if one is allowed in the U.S. to post a streaming audio file of a personal arrangement of a jazz standard for non-commercial promotional purposes on a website? For example, if you have an arrangement you made as an assignment for a college class on big band writing and the piece was recorded privately at a reading session, are you allowed to post the recording on your website not to be distributed, but as a streaming example of your compositional abilities? Do you need to obtain some type of authorization/permission before you can post such a file, or is this within fair use?

Anyone?

Or, there's this question: is there any good reason for putting "All Rights Reserved" in your copyright notice? I heard that the phrase can serve as some form of copyright protection in countries outside of the U.S., but I don't know if it holds true anymore (if the phrase is automatically assumed and thus unnecessary to use). Also I've been seeing a lot of works with "International Copyright Secured" before "All Rights Reserved." Can anyone comment on the purpose of using these phrases (and comment on how you secure international copyright; I am under the impression that there is no true international copyright since most countries do their own thing).