Steve, to amplify and add to what Colin said... when I got started with Moodle a few years ago, I got a free hosting account with HostGator (unfortunately, they've decided to end the program where they provided a year's free account to non-commercial or educational organizations). That not only got me a web site that I could use for all of the things that web sites are good for, but also a Moodle installation that took only a few clicks in the control panel to set up. It really is very easy to get going, plus with deference to the 'free' hosting sites, a commercial host vendor will usually have more than one data center with disaster contingency protocols that insure that your site and course stay available in almost all instances. For $67/year (in the case of my paid Hostgator account) that reliability is definitely worth it.
Good luck with your endeavor.