As everyone else had said, getting a web host and domain name is fairly straight forward. If you don't want the hassle, most website desigers these day will source the domain and web hosting for you, but will want to add a little to the price to make it worthwhile.
For the domain name go with either 123-reg or 1and1, and then choose whether you want a .com or .co.uk. If you can afford the .com then go with that (about £18 for 2 years), but the co.uk (£6.00 for 2 years) will be fine.
If you are not bothered about who you host with as long as its cheap, I'd go Siteground, they're US derived, but a bloody cheap, maybe the cheapest around for the quality of service they offer, which is high.
If you want a UK host, there's plenty of them around, but you will pay anywhere from £30 to £100 a year, so shop around for a good deal. Once again a web designer would be happy to do this for you, if they are not already an affiliate of one company or another.
As for the website itself, if you want a nice clean, functional site, that is simple to manage, go with Wordpress or Joomla. Both can be built on a budget, but still be prepared to pay £200 to £500 depending on the designer and the level of specification you want.
In the past I have done a 4 page Joomla site for as little as £200, but to be honest they are basic, but once again if you shop around, you can get quite a lot for a few bucks. Like everything else though, spend more to get more. £300 to £500 would get you something nice and easy to manage.