Hmmmm ... you've never run Windows 3.11 or below, Windows 95 or 98, nor Windows NT 4.x server, huh? Does Mircosoft still provide that 'extra CD' that contained all the small (execs) for administering a server for which there was no GUI app? Ya see, it's been years since I've even looked at a Windows server ... guess that kinda describes where I'm coming from, huh? But ... read on, please ...
While you could install a GUI desktop on a Ubuntu server (LTS version), for your specific purpose, the GUI desktop doesn't give one any advantage in running a Moodle (or a Joomla, or a WordPress, etc.) ... and here's why ...
Moodle (really a series of php scripts) runs best under apache, mysql/postgres, and of course, PHP. Apache is a faceless server daemon as is MySQL. The only GUI with MySQL is a client applications which one could run from a Windows/MacOSX/or Linux workstation.
Configuration of Apache, MySQL, and PHP is all done via editing text ascii files .ini's, .cnf, or .conf with a text editor. All one does with them is set a parameter ... like seconds a php script is allowed to run.
Besides that ... most server administrators want ALL the resources of the server to be dedicated to the purpose of the server ... serving Moodle. Those little applets for a GUI clock, screen saver, etc. on/in the GUI desktop just take up cpu cycles and processing power away from Moodle ... ie, MySQL, Apache, and PHP.
Besides ... one can find PHP scripts to help with some things ... like phpmyadmin ... I, personally, like Webmin to help administer a Linux server when I'm feeling lazy.
And one more ... when it comes to apps like Moodle, it's really tp of the iceburg when installing ... thereafter, comes backups (code directory, DB sql dumps, and data directory) and updates - both of those more efficiently/accurately accomplished via command line tar, mysqldump, and git.
Command line will grow on ya.
My 2 cents of course ...
'spirit of sharing', Ken