Kim and Jeff,
With wordpress.com, you sign up for an account and a blog, both are which are free. But, that gives you a site like www.yoursite.wordpress.com
or something like that.
With WordPress (.org) you install the wordpress blog site on your server in your domains directory so it resides in yoursite.com. Just about every good hosting company out there has auto-install functions for many many types of programs (blogs, forums, shopping carts) for free.
Personally, I prefer bluehost.com for hosting companies, but any good one will have the above.
With a wordpress.com account and blog you will be very limited in how much customization you will be able to do.
With a wordpress (.org) installation, you have a supply of endless themes (how the site looks) and plugins (add in applications that give your site more functions and features).
Some good WordPress documentation:
WordPress Themes directory (you can also google 'wordpress themes' and find many more on the net):
WordPress plugins directory:
If any of you need in depth help with WordPress, feel free to send me a pm and I'll do whatever I can to help you out.
Also, if any of you are interested, I'll share the list of plugins that I use that I think are essential for any wordpress site (and included in any wordpress site I build).