Registering the domain if it is free, will cost arouns £7, I use godaddy.. can get emails on it, people use whatever.. it does not make a difference.
You can then find hosting for a few £ a year with google, if it will just be one page you can go for the cheapest.
get a cheap .info domain main.
If thats all you need it for, then get a .com domain from Dynadot.com and set up URL redirection to your Linked In profile or get some basic web hosting for $11.99 a year and you can get email accounts too and put your own website up.
If it's really that small, ask around your friends if any have a website. I'd certainly host a small personal website for a friend for free, including an email inbox.
Then all you need is your .com... reliably cheapest I've found is namecheap.com - $10 for a year with free whois protection if it's a .com (means someone can't look up your personal details by doing a "whois" query on your web address) which translates to £6 - £7, depending on exchange rate.
Personally I'd always pay the extra couple of pounds for a .com over a .co.uk, .net, .org etc... it's just what people are "used to" with decent sites.
You could try freewebs/Webs.
GoDaddy always have deals on. You can find infinite amounts of discount codes on the web too, I signed up to their mailing list and always get emails telling me about how theres x% off.