WordPress is an open source blogging platform that you can download and install on your own hosting account. It will allow to customize it to your heart’s content, while providing you with the same power you get from WordPress.com.
WordPress.com on the other hand, is a free service that allows you to have a hosted WordPress site on a subdomain within WordPress.com (e.g. myblog.wordpress.com). With this setup, you get a free blog that is super easy and fast to setup and get going. However, you don’t have the same freedoms to modify the install as you do with your own custom install of WordPress, on your own server.
There are 2 other major downsides to using this (or any) free blogging service. The first one is that you are not building up your own SEO and brand. The second is that you do not actually own the content. If you check these free blogging site’s TOS, you’ll find that in using their system you agree that the content belongs to them, and thus, they can take down your blog at any time, and there’s nothing you can do about it (except to beg their technical support to give it back to you).
So I definitely recommend that you build your main blog site on your own server, and use your own install of WordPress. Any PHP/MySQL host will do, but I recommend using HostGator. Once your hosting account is setup, then use their cPanel to easy install WordPress, then your guaranteed that everything about the site, including the content belongs to you, while allowing you to build up your own SEO campaign and brand…