Namecheap is great for registering the domain. Go Daddy will nickel and dime you to death! Wordpress is more of a platform, so you'll still need a hosting company. We've used InMotion and Bluehost lately with success. You'll want a hosting company that can easily be used with FTP (File Transfer Protocol - an excellent and easy to use FTP client is FileZilla plus it's free!). With FileZilla, after the initial setup, it's just a matter of connecting then drag and drop just like you would on your desktop. You should be able to set up a guest FTP account with your hosting company too, so someone else can add media (if desired).
To summarize:
Step 1 - Use Namecheap to find a good domain name (like theglynproject.com)
Step 2 - Find a hosting company that supports Wordpress
Step 3 - Download and install FileZilla
Step 4 - Setup a Wordpress account using your domain and hosting company
Step 5 - Create a basic website using a Wordpress template, find a knowledgeable kid to help, or pay through the nose for a professional site (a "real" business website starts at $5,000 and goes up rapidly from there!).
Step 6 - Use FileZilla to upload and manage your media.
Good luck Glyn!