I've tried to install "Moodle" to a free web hosting sever and my proper website as well so many times, but I wasn't successful at all. Sometimes I had problem with PHP settings (safe mode), sometimes with "moodledata" folder (can't create it or wasn't safe enough for the installer) and even if I used ssl connection to upload every files, it took ages.
But finally I find a really nice and easy solution. You don't need to create any database and you don't need to upload anything. Just few clicks and you've got a proper Moodle site.
I hope you find it useful.