Do not go the WordPress.com or Blogspot.com direction, it's counterproductive.
Either create a directory on your current site, or snag a domain and a hosting account and install wordpress or textpattern, wordpress being the easier of the two, which literally takes 5 minutes. I suggest installing into a subdirectory, since you can still show it toplevel if you wish, it makes it easier at upgrade time.
For wordpress you'll need Linux/Apache/Mysql/Php hosting. They say it'll install on Windoze, which is somewhat true, but many of the best features don't work well.
Go into your host's control panel, create a database, a user with password, and add the user to the database. Rename and edit the config.php file to reflect your database info. Upload all wordpress files into your chosen directory, then simply call that domain/directory in your browser. It'll ask if you wish to install, which you do. A username, email addy and you're done, just make sure to save the password and use it immediately to get into admin to change it to what you wish. Then start blogging.
I've got some
free wordpress themes, released under Creative Commons for noncommercial use, on my site if you want to change your look.