Your asking about two different services. Domain registration and Web hosting. If your a beginner it will be simpler to buy both services from the same company. It's the hosting part you need to look into as this even for very cheap hosting it will cost you 5x more and there are more options to consider with hosting.
Assuming your site is going to be simple go to one of the big name hosting companies and buy their cheapest package. The large companies are used to dealing with beginners and will have help articles on their site to guide you through. In the UK big consumer hosts are 123-reg,1&1 and heart internet. I don't know about other countries, unless you have reason not to go with a provider in the same country as you are located.
If you planing a complex site that would cause you financial loss of it went down then employ a professional.