Hi John,
Less than a week ago I asked TMDHosting to back up and upgrade our DE site from Moodle 2.2 to 2.7. In about 12 hours our site was accessible again. I learned from the upgrade experience from others and applied their knowledge when I faced a blank page at log in (did a clean installation of the Moodle 2.7 software package without any plugins) and a warning message that Moodle cannot downgrade to a lower version of a module (manually changed the version of the module).
For almost six years we are hosted on a shared server with an SSL certificate for $12/month at TMDHosting. I can highly recommend their service. Support tickets are answered within 15 minutes. They have very competent people who will do the installation and upgrade of your site much better than any one-click installation can do, but they will not answer all questions or do everything for you.
Stay away from automated backups (Moodledata and Moodle DB file size may increase enormously). Instead I recommend you to learn how to back up Moodledata, the Moodle DB (all explained in Moodle documentation) and to install Moodle in a local installation (I use Bitnami) so that you can mirror your site and test the upgrade without risking your life data. Before you are going to upgrade your site, you should read what challenges others have experienced with their Moodle installation. I have no formal education in computer science and have to look for financially affordable solutions. I learned a lot by reading through Moodle forums and I am very thankful for the people who share their experience here for free.
With kind regards,
Hartmut