You have many choices. You can either have your blog hosted by someone else for free, or you can host a blog on your very own site. I would highly recommend that you host your own blog on your own site, and here is why.
First of all, Blogger and WordPress will host your blog for free and it will even allow you to park your very own dotcom name to point to it. But the problem with this is that you are building someone else’s site. They could shut the site down at any time if they decide they don’t like you, and you have limited control about what exact themes and plugins you use on this blog. It’s easy to set up, but you have less control.
If you host your own blog on your site, you have a lot more flexibility as far as extra plugins, extra themes, and you are not at risk of being shut down as much. What’s great is that if you have a cpanel webhost, there is a section called Fantastico that will allow you to install a WordPress blog anywhere on your site with one click.
The good news is that when it’s installed on your own site, it does not promote anyone else’s site and you can easily move it anywhere you want to a different domain main, different webhost, whatever. Even though Blogger.com and WordPress.com make it easier for you to get set up, you have less control and it’s worth it to take those few steps to set up your very own blog on your very own website.