Your domain name needs to include the niche you intend to work in. If you are building a website about golf balls then it might be www.BestGolfBalls.com or www.ProGolfBalls.com.
Only search for the exact name once you are ready to buy. There are ways to monitor domain name searches and there are people who will buy names that have been searched for so they can then blackmail you into paying ten times the price.
If you are targeting world-wide or US users then only buy .com domains. These give you maximum credibility.
National top level domains like co.uk are good if you are targeting users in that country, but most of these require you to have a physical address in that country.
Avoid strange characters like – (hyphen) or _ (underscore). People never remember them and your site is doomed from the start.
Make your domain name as short as possible and easy to spell. For example, if you are doing a site about “grass” then www.GrassSuperstore.com would not be a good title because of the three “S” combination in the middle.
Many two word combinations have been taken by speculators who hope to sell them on at ridiculous prices. Good three word combinations are still available if you are creative. Writing Paying Articles is a good exabecause it covers two different search phrases; WritingArticles, and Paying Articles
Avoid possible legal disputes by staying away from brand names. www.SonyProblems.com is going to attract the attention of Sony’s highly-paid lawyers. Even if you are doing nothing illegal you cannot afford the court battles that will ensue.
It is better if there are two people sitting at the computer when you are buying your domain name because the second person might spot confusing possibilities or spelling mistakes that the first person misses.