I suggest WordPress, and if you want to start out with a simpler version of Wordpress, to get the hang of it, then you can try using their older version of 1.5.2. Of course, they don't really provide support for it, because it IS an older version of Wordpress...

http://wordpress.org/wordpress-1.5.2.zip

Next up on their ladder of releases, is version 2.0:
http://wordpress.org/wordpress-2.0.zip

Then of course, the rest follows, up to their latter releases...
http://wordpress.org/download/release-archive/

Some helpful guides as well...
http://www.tamba2.org.uk/wordpress/

Like the others stated above, self-hosting WordPress is the way to go, if you want more user control over your blog. If you don't care about that, then you could try using Blogger first. Or, a free blog on http://wordpress.com. Just sign-up, tinker around with it and etc. However, I think all blogs on wordpress.com, run their latest version of WordPress, which really isn't "simple" to a starter person.

Usually they keep wordpress.com blogs, updated to their "unofficial release" versions of WordPress. Which could be version 2.8.X or what-not. But that's when the top developers are feeling frisky. Good luck either way!