When choosing a domain name you need to consider what you are going to use it for.

Email only Domain - you don't even want a website - just a unique domain name for an email address.   Choose a domain name combining two words - your name maybe with an initial - and use hyphens as separators.   So you could choose fred-d-bloggs.co.uk.   Not wonderful, but its yours and is the best available.

Restricted Access Site - you want a website that a fixed group of people will use - and you can tell them all what it is and where to find it.   Choose a domain name combining two or more words - and use a hyphen as a separator.   It doesn't matter about being a little long or not catchy as all your users can bookmark it.   So you choose swdivers-club.co.uk for the South West Divers club.   If that's gone then choose sw-divers-club.co.uk.

Commercial Site - you want a website that gets listing in the search engines and you want to attact customers/visitors to use you site.   Again choose a domain name combining two or more words - and use a hyphen as a separator.   Its best to choose a domain name that describes the concept/theme you want to promote.   So for selling duiving gear you may consider diving-kit.co.uk or diving-gear.co.uk.   You should also consider getting the full suite of domains for that name - .co.uk, .org.uk, .com, .net and .org if available.   If you don't, and are successful, someone else will..   The key here is that the domain name no longer needs to be snappy and catchy.   All the good domains have gone.   So choose a search engine friendly domain name instead that fite with what you are trying to sell/promote.   You are going to be promoting your website by means other than the domain name itself.   You only really need consider buying a good domain name when you are using it for brand development where most of your advertising and promotional activity is not internet based.  

What Next?

Use the domain finder on the right to find a domain name that suites you.   Don't buy it yet- you should in general use the same company to buy your domain name and host your web site.   If it's been available till now -it won't go in the next few minutes.   Then go on to the next section to learn more:

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

Buying a Domain that's already Registered

You can look on the resale market for a domain.   Most domain names are for sale at the right price.   The links below are to the best known reseller sites.  

BuyDomains.com
Moniker.com
Sedo.com
GreatDomains.com