Hi Paul
i run about 50% of my sites on wordpress. a few things you need to know. you will need to get a web server with cpanel which will have a button on it called "Fantastico" which will do all the set-up for you.
first you need to go to 123reg.co.uk and get your domain then go into your domain control and you will find the link to your nameserver point this to your server account. you will get the details of your nameserver in the first email you get when you set up your server account.
next go to your cpanel and into Fantastico fill in your domain details, and that's it. you can add HTML sites to your server by FTP which again the details are in that email. The program i use is free and called CORE. just reg your domain then got to cpanel and into add on domains fill it in then open up the ftp and log on where you will see a folder with the same name as your domain put all you site files in it and your up and running
http://www.coreftp.com/Richard be very careful about buying domains though third party's some will register their details and you don't own the domain. i had this once and spent many months building up the domain only to lose it at renewal when the company put it up for sale.
Paul if you use shared server space its risky as hackers can get in much easier. get your own server. this way you are in control of all the software updates which is the number one reason people get hacked. by not keeping any software updated you will be a risk.
what happens is that when a hole is found in any software hackers pass this info around to each other. they they build spiders to go out and find sites with the old versions on them and hack them. I have had this problems a few times. as soon as a new version come out update. when you are on shared servers your not in control of this.
other advantages of your own server is your own IP address and if you want to have more than one site you can add more. which helps is SEO a domain with its own IP is an advantage. think of sharing a server just like letting other people share your PC. as you will see that's all a server is a rack PC it has memory hard drives etc
good luck
Respect
Ian Harper