Our servers meet all the requirements for installing the latest version of Moodle. Several customers have specifically told us that it works well for them on our servers.
You should be able to install and run Moodle following their standard instructions. You should also make sure your account is set to use PHP 5 instead of PHP 4. This page explains how to do that.
When you configure Moodle, be sure to disable "course backups".
According to the creators of Moodle, "course backups" are not the preferred way to make regular backups. The preferred method is "site backups", and we already make site backups of your Moodle files and database every day, automatically.
Turning on unnecessary "course backups" will slow down your site and cause extremely high disk and CPU usage. If your site is accidentally set to make course backups, we will disable that by adding this line to your Moodle "config.php" file:
$CFG->disablescheduledbackups = true;
(We'll notify you if we do this, of course.)