jarrodr, normally you would use Joomla for more than just a static website, so it might be a bit overkill for your project?
But, to host Joomla sites you need to look at a Linux host, with PHP 5 (preferably), MySQL, as per this list:
http://www.joomla.org/technical-requirements.html
Generally, if the host offers cPanel + fantastico (or Softacoulus / Installatron / etc) , then Joomla will work "out of the box". Other control panels may also work, I don't know, since we only offer & support cPanel at this stage.
We can offer you ZA based hosting if you're interested.