Okay, this will be slightly complex, but not too bad.
1) Why not purchase your domain name? Since you have bought from GoDaddy, they are probably sending you discount promotions, like 20%, 30% 40% off new purchases. If you think you are going to have this site for awhile, consider buying your domain name for 5 years at the discounted rate.
2) I too have WHM and cPanel. WHM controls your overall site, cPanel controls one user. This is good.
3) If you ever need to reboot your server, in WHM goto System Reboot | Graceful.
Here are my notes about what I did in WHM. Some of these are optional, but see how far you get.
Things
to do in WHM:
Go to Account Information | List Accounts. If there is no account, you will want to create one for yourself. For example, I created one for rjerzcom. This then becomes the account where I will install moodle. I image all of this can be done as "root", but as a novice I have learned that doing things as root can be dangerous. So I install Moodle as rjerzcom. (my domain, incidentally, is rjerz.com).
(optional) Change the timezone, Home|Server Configuration|Server Time = America/Chicago (for example).
(optional) Add yourself (in my case rjerzcom) to “wheel group” users, for su access.
Try ssh to server. This is important. You will want to be able to ssh to your server as yourself (in my case rjerzcom). In Terminal (Mac), I try ssh rjerzcom@mydomainname.com, password, success. This is where you will be installing your moodle, as a user, not as root.
Try switching to su while in ssh. Issue "su", put in the root password, and see if you have success. At this point, as su, you can do a "yum update." Remember if anything goes wrong on a new server, you can always reprovision your server to start from scratch. I find that it is important to be able to ssh as yourself, and then to be able to switch to su because some administrative tasks have to be done as root.
Back in WHM, find "Easy Apache." This is an important and nice utility. From Easy Apache, you update apache and php, and turn on all the required Moodle directives. I added: zip, xmlrpc, soap, mysql improved, mbstring, intl, gd. These are all needed for Moodle. It may seem like a scary step, but do it. Right now, I am using PHP 5.5 and Apache 2.4 (I see that I have to click on the "gear" to make changes.) I would pick something like php 5.5.32, and then in the exhaustive options list, turn on the directives that you need.
At this point, if you are successful, you might want to try FTPing to your account (as yourself). Sometimes FTP is handy to be able to do.
Now even though the above might seem difficult, you are basically ready to install moodle. You see, these steps make sure that your server is ready. If you don't, for example, install the php directives, Moodle will complain and not install. On a GoDaddy hosted server, some of these steps are automatically done for you, but not on a VPS. GoDaddy assumes that if you buy a VPS that you know to how to do these things on your own.
Someday, I plan to make a video showing these steps. The "expert" server administrators will probably have their own ways of doing these things, but I am a novice. Actually, I am a professor, not a system administrator.
Before I go on, however, let me know if you are having any success with the above steps, please.
If you are successful gaining ssh access to your account, you should be able to type "ls -al" and see a list of files and directories, maybe 20-25 of these will show. You will see a folder public_html. This is where moodle will go. It is your website, too.
Tell me, would you like to install moodle in www.yourdomain.com/moodle? This is what I do. I then find it easy to update moodle in the future. But some folks want moodle to appear at www.yourdomain.com.
I will be back with you after you report your progress. See you again soon.