Seeing as everyone wants to milk you, let me add a quick tutorial to this:
Registering a domain name:
First you'd need to have a DNS server (this resolves the name into an IP address where your hosting is). Don't be alarmed, this normally comes with the hosting OR with the domain.
Registering a domain. Would it be a ".co.za" or a ".com" (or any type of international domains)
If you're going for a .com, you can register with Godaddy.com for cheap, they usually supply their own DNS servers which you can manage yourself (it initially points to a "hold on to your tits this website is almost here" page

)
If it's .co.za it *can* become complicated but it's as easy as sending an email, however, you'd need a DNS configured with your domain first before sending the registration email. (
http://co.za for more information)
And hosting... ask these guys. They would probably supply you with your own DNS server as well as web space and most probably register and charge you the domain name too.
For .co.za however, it's easy enough to register yourself (if you already have hosting with a DNS configured with the name) and only costs R50.
If one of these bozos (I say this in jest guys) charges you anything more than R75 for this registration "privilege" they're taking you for a ride. I've seen guys charge up to R650 JUST for registration of the domain that costs R50!
Also, make very sure if you're doing the .co.za thing that the hosting company does NOT put their details as the "registrant" details on the info
This is against the terms and conditions of Uniform and would most likely (if there would be any future disputes over who's domain it is) end badly for you.
And as an added tip. Install IIS5(or 7, depending which Windows you're running) and start learning more about web server, dns servers and firewalls/ips and domain registrations (ports, emails smtp etc)
The world is full of people who think they can "do websites" but there isn't many who can understand, configure and troubleshoot issues effectively enough. Most basic thing is to learn how to FTP at least.
Currently working with 2 web designers who doesn't know their elbow from their ass and it's frustrating trying to explain to them how to FTP their files onto the web server, which makes me highly doubt their ability as a
web designer in the first place.
Good luck!