You have a copyright automatically when you create a work. However, if someone steals your stuff and you want to take them to court, they could bury you in legal rigmarole unless you have deep pockets or good proof. The best proof is an official copyright registration. It also helps to have witnesses who will testify that you did indeed create the work, in cases where two different parties register the same material. (Collaborators would make great witnesses. Hux could testify to the validity of the CC forum records, should they still exist at that time.)
Any citizen of or person publishing material in any of the Treaty Countries can register their copyright with the US Copyright office. It costs $30 per application.
You can bundle any number of songs on one CD for registration, but only if ALL songs have IDENTICAL ownership. For example, if I wrote all the music and Fred wrote all the lyrics, they can all be registered at once on the same CD (for a single $30 fee). So divide up your songs into CDs where the ownership is identical for all the songs on each CD, and submit an application for each CD separately. Each collection needs a title and be sure each CD is clearly labeled with its title.
Register the CD as Performing Arts. This protects the CONCEPTs (which is the most important thing to protect). The short form should apply in most cases, just use that form and read the instructions at the top -- you'll find out if you need the long form.
You can also register the CD as a Sound Recording. This protects the particular performance or rendering of your song. You can even do this in the same application (same mailing envelope, same CD -- I think ya still gotta cough up the extra $30). This is the only protection you can get for compositions you don't own, such as your recording of Proud Mary.
In various places, the forms and instructions talk about "published works". The specific status of publishing on the web hasn't been established, but it's not really important here, where they're really talking about "printed" as in produced as a product. If you've only published on the web, consider it "unpublished" in the applications.
If you want to buy the right to publish your rendition of someone else's composition, you can get a compulsory license (also called a "mechanical license"). The easiest way to do this is through the Harry Fox Agency. The cost is a $10 fee for Harry plus the legally dictated rate. The rates go up every few years; right now its 8.5 cents US per song or 1.65 cents per minute, whichever is more. [This applies to any originals that were published or distributed in the US.]
Note: I am not an attorney. This is my careful interpretation of what I read on the US government website, www.copyright.gov. Don't omit the "www".