After carefully examining many domain hosting providers and listening to advice (thanks Scott Hanselman!) I have finally made a choice and joined 1&1.
I wanted a cheap service just first to try out and satisfy my basic needs. It turned out 1&1 is a good provider. The interface is relatively simple, but functional, the website builder is good, so I am happy!
As a result my personal web page is now online at www.zubarev.net, you are welcome to visit!
Interestingly, this provider supports web page access with or without the WWW. An interesting article on this topic you can find here: http://www.codinghorror.com/blog/archives/001109.html