As long as you have a registered domain, you don't have to host off wordpress.com. Do you already have a registered domain?
Wordpress is a CMS (Content Management System), basically its just used to keep all of your content organized (there is much more to it, but thats the gist of it) and allow people without web dev knowledge to manage your website/blog. It can easily be installed in under 5 mins in a very user friendly fashion at most hosting sites. I recommend Media Temple.
Most shared hosting plans allow you to have multiple installations of WordPress. If you have CPanel as your admin interface, you can go to add-on domains if you are using separate domains, then go to Softaculous to install the various instances of WordPress. One of my hosting accounts is with eleven2.com and I have 15-20 separate WordPress sites there on a $10 a month shared hosting account. I've got a similar setup with MediaTemple. I believe this is similar with GoDaddy, Hostgator and other platforms.
Check out Media Temple who are currently offering free site movement as well as 3 months free hosting. A bit more expensive but the best support and uptime I've ever had.
I prefer MediaTemple, been using them for about a year after coming from Dreamhost (ugh). MT is spectacular, and I believe they have WordPress as a one-button install!
Give it a try: http://www.mediatemple.net/#a_aid=4f1a3728a813b
asmallorange.com is pretty nice, and they're redditors.
Personally I use mediatemple.net - it's $20/mo but has features upon features upon features. I host about 10 smaller sites on the same account and just built the first year of hosting into the price of development - so I actually make money off of it anyway.