You could also use a free hosting service, which will not require you to go through the domain registration process. You will not have your own domain name, but you will avoid ever having to give out billing or contact information. Sites like Blogger.Com, Wordpress.Com and even Hubpages.Com are a good place to start.
Secondly, never post a message from your internet connection at home or work, since the IP address can easily be traced back to the original source. Your best bet is to compose material offline (in advance) then travel to an open Wi-Fi hotspot to actually upload the content. If you are really paranoid, I'd avoid any hotspot that has security cameras nearby and utilize software settings that generate a new MAC address for your laptop or netbook every time you log on.
If you WERE doing something illegal, or at least something that you would never want anyone to ever be able to prove you did, be sure to never write any of this data to a hard drive, as computer forensics can easily un-delete anything on it. Your best bet is to compose everything using a "Live CD" Linux distribution (i.e. Ubuntu, Puppy Linux, Helix) that runs everything in RAM and then save the material to a cheap, disposable thumb drive or flash memory card.
Obviously, avoid using your real name or e-mail address when registering on free hosting sites. Use the above techniques to get a throw-away address from Yahoo!, Hotmail, etc.