Domain names can be split into two groups.   There are the top level names you can buy from true registries, and then there are the sub-domain names.   Make sure you understand the difference.  

Top Level Domain Names - are split into two groups: the gTLDs and the cTLDs.  

The gTLDs - generic Top Level domains - are used globally and consist of the .com, .net, .org, etc.   Many people think of these as the USA domain names, but they are actually generic and used all around the world.   There are more .com domains than any other type, so the chances of finding your .com are slim.   These are also the most expensive to buy in the reseller market - some are worth millions of dollars.   All these domains except the .eu domain are run from the USA and their use governed by US based organisations.  

The cTLDs - country Top Level domains - are specifc to a particular country and the rules that govern them are country specific.   As this web site is aimed at UK hosting, the country cTLD for the UK is .uk.   The UK cTLD is run by Nominet and divided into .co.uk, .me.uk, .org.uk - available to the general public, and .sch.uk, .ac.uk and .gov.uk which are resticted.   There are few restrictions on the purchase of .uk domains - anyone can own them and they are cheap.   The two largest cTLD domains are the .de and the .uk domains.

Sub Domains - there are several of these dressed up to look like real TLDs.   The common two in the uk are .uk.com and .gb.com domains.   Understand that you are buying one of these, that there is greater risk that they could disappear, and that the company that runs them has final say over who owns a particular sub domain name.   You will also find that they are quite expensive.  

What Next?

Now you need to choose a domain name.  

Choosing a Domain Name
How to build your Web Site
Choosing a Web Hosting Package
Reaching Your Audience - Getting Visitors to your Site