Automated full site backups ... that's code, DB dump, and an archive of all folders/files contained in moodledata. On a shared host you probably also have inode restrictions (number of files in your account) as well as a space restriction ... full site backups, depending upon site usage, could total to be more space than your account allows.
When your server reaches whatever maxes are in place on shared servers so users on such systems cannot use more than their 'fair share', what will happen? Will provider deny access to your server? ... or send to you an EMail telling you that you must remove files? - ie, free up some space or risk having your server shutdown ... no longer accessible.
So before any begins to give you idea as to how one might be able to do automated full site backups, think you need to read the fine print of hosting provider.
Think your safest approach, should you decide to stay with hosting provider, is to make regular full course backups and download them to a local computer.
'spirit of sharing', Ken