I created my website using Wordpress. Although it is primarily a blog software, it can still be used to make great static websites. Lots of plugins and themes available. There are sites that handle all of the setup and hosting for you, but if you want to setup wordpress yourself, it's not too difficult with their 5 minute guide and some googling about. Joomla and Drupal are also popular options, but i'm less experienced with them.
Weebly is another one that is pretty easy to use and more designed for static websites, rather than blogs/message boards. They handle all of the hosting and setup for you. They offer a free plan and the paid plans are pretty reasonable.
If you're looking for a free domain name, check out Dot TK - Free Domains for All
. Although, I'd recommend getting a real .com,.net,.org right off the bat. You don't want to be changing your name after your site takes off!
Hope that helps.