Anything you create is your copyright. However, when you create a derivative work based on someone else's copyrighted material, you are essentially at their mercy when it comes to making any money from it. Musicians who sampled mere seconds of another band's work without prior clearance have found themselves stripped of all royalties and publishing rights. So it goes with fanfic, too.
If it's original fiction (or any other original kind of art), it's your copyright whether you register or not. Registration makes things easier if you ever need to sue someone for infringement, but US copyright law provides that you need not do anything special to copyright your work and have legal protection for it.
All rights are reserved by default. If you post something on your own website, with no notice of what rights you do and don't reserve, you are indicating others may peruse your work but may not copy it (beyond downloading pages from your site), derive works from it, or commercially exploit it. If you post on a public forum owned by a third party, your work is governed by the terms of service of that site, which you agreed to beforehand.
Many publishers (not necessarily all) want "first publication" rights, meaning they want stuff that has never been published anywhere--including the Internet. If your work has enough commercial potential, they may overlook this. It is also not totally unheard of for someone to self-publish a book and have it sell well enough to get the attention of a major publishing house.
