If you are not familiar to non-GUI servers (text only), and you are going to use LAMP (as mentioned in Moodle's website) in order to host your web site with Moodle (or any other CMS like Joomla, Wordpress, personally I can't say the differences or special powers of Moodle). So you should try Ubuntu Desktop (common version) and make it run no desktop environment nor GUI at all in the boot.
This way, if you need to do something, you can simply start the GUI and your favorite desktop environment in order to do whatever changes/testing you need.
If you choose to install the server edition you may be able to use non graphical tools to admin your files/folders (midnight commander for browsing, nano, vim/emacs to edit files and a lot of useful text based tools).
I can't provide any support for the remote administration account but if you install online services you can edit web files directly from your webpage. Check the eXtplorer project for file browsing/editing, phpMyAdmin for editing MySQL Databases and if you have a special need please drop a new question with such need in order to get the proper support.
As everything is running to be online (such as documents in web services, etc.) you should consider installing enough services that allow you to do whatever you need. There are services for editing your PHP, HTML, CSS and other popular files directly from the website so that you won't be in need to gain access to the server just to make small changes. However, you must consider to gather the proper support in order to have the remote administration account in order to be able to run powerful tasks directly on the server.
What I mention is based on my own experience using a desktop web based server on which you can gain access to the files/folders and certain administration (like files/folders permissions, etc.) just by using web based services like those I have mentioned over here.