about these issues - many people find themselves lost when it comes to sorting out their own domain name and hosting.
As you've discovered, the 'main' domain name suffixes - like .com and .co.uk and .net have long ago run out of really significant names, and it's increasingly difficult to find anything that's of much use. We've seen other suffixes appear over the past two or three years - a notable one for us was .eu.com - and these have enjoyed varying degrees of success.
If you want to run a commercial site you really do need to find a name in the big three or four high levels (.com .co.uk or .net) if you want to make an impact, although I have registered quite a few .eu.com names for clients of mine over the past two years or so - it's becoming an increasingly popular suffix.
If you simply want a name for a personal site, then .me.uk is fine, but it has little or no impact as a commercial suffix.
You can register your name with one company and host it with another (or organise domain forwarding) but there's little point in that - you'll find that any good host will register your name for you as a matter of routine. It's far better to keep everything under one roof, and you don't have to get involved in moving the name around from one name server to another.
My current web-host of choice is HeartInternet
I've used most of the big companies over the years, and I've finally settled with HeartInternet (I have a reseller account with them) as being about the best I've tried. The better-known hosts will all offer you a broadly similar package, and it's never easy to choose. I used 1&1 for a while, but to be perfectly honest I had considerable problems - mainly with FrontPage sites - and I found the customer service didn't always live up to expectations. I may have had an isolated bad experience of course, but since moving my sites to Heart I haven't had a single problem.