Copyright is automatic upon creation of the work. However, proving it is another thing, and he with the deepest pockets could win. The "poor man's copyright" (mailing the work to yourself via
registered mail and not opening it unless having to demonstrate proof of copyright in court) could provide some level of proof, but most (including lawyers) suggest that this is not adequate.
The only absolute protection is registering the song with the Library of Congress Copyright Office. Last I checked, it was US$30 per song. You can copyright a 'compilation' of songs for the same fee (any number, I believe). This may be the better and more economical route if your intent is not to ultimately be the recording artist representing the song, preferring to shop the song to publishers for other artists to record/release. Then, it must be remembered that upon signing of the publishing contract, the copyright for a particular song will be assigned to the publisher (with negociated 'reversion clause', usually 2 yr. max., in case the song doesn't get cut). It's the publisher who then 'again' registers the copyright under his/her pubco's. name.
Here's the link to the LOC Copyright Office form download web-site:
http://www.copyright.gov/forms/. I believe you need either
Form PA (or the short version), or
Form SR depending on your situation. Of course, all the copyright info you need is available via the LOC Copyright Office. It may even discuss the "poor man's copyright" somewhere there.
Good luck!