I just finished building my first site hosted on my own domain. I used Bluehost as the hosting company to register the domain name and then used their simple scripts to install the Concrete 5 CMS. There is a simple script for Joomla too, which is a more commonly used and sophisticated CMS, but Concrete 5 is more user friendly.
Speaking as someone who did this for the first time, it's not a really difficult thing to do. Once you've got your domain hosted and use a simple script to set up your CMS then you just need to choose a template for the website and start plugging your content in.
EDIT: Here is a link to
the website I built. It's not extremely sophisticated or anything, but I just used a free template for it. The process of building the site is very quick once you've got your content ready, and there are a lot more really nice looking templates that you can find with either Concrete 5 or Joomla if you're willing to drop a few bucks.