The domain name is your web address, the www.mynamehere.co.uk thing. It should not cost more than £10 for two years and it should always be registered in your name, not the web designers.
It should include what you do. Google reads the words in your domain name and compares it to the content of your website. It should be relevant to the web site content, Google uses this as part your Page Rank (Page Rank is Google’s scoring system). As such your domain name is part of your Search Engine Optimisation (SEO).
It is also useful for letting people know what you do at a glance i.e.
Which one is more informative?
Try to break words up with a hypen – it makes it easier to read and also stops other words forming by mistake. The most famous case was a shop called Pen Island, when you put the two words together you get ‘penisland’ I think you will agree ‘pen-island’ is safer and easier to read
It is always advisable to buy two versions of your domain name and point them both at the web site.
www.acmeplumbing.co.uk easier to say over the phone, but www.acme-plumbing.co.uk looks better on your business cards and stationary.
123-reg are a cheap and reliable domain name seller and you can check for free if the name you require is available. I normally buy my domain names from 123-reg and host my website with Host Gator – even though it is in America, it still manages to serve up your pages lightening fast.