After you decide on the subject of your website, the next step is to choose domain name and domain extension. All my domain are .com domains and for vast majority of websites .com is the best extension. Domain name is important. You would want domain's name that is easy to remember and easy to spell. Ideally, it should be no more than 3 words and no longer than 15 characters, not counting the extension. The shorter name is better than longer name. You would want domain name to reflect subject of your website. Many good short domain names are already taken, so to find good domain name may not be an easy task. It is helpful to get some keywords into your domain name, even more so if you are planning to get paid traffic.
Another approach would be to choose one or two short words, that would be unique and easy to remember. I would suggest, that you create a list of domain names, that you like and check, what names on that list. if any is available. I buy my domains from GoDaddy and they have domain name generator, that tells me what similar names are available, if one I am searching for is already taken but you can use any domain name Registrar that you like.
If all good short domain names are already taken, should you buy good domain from current domain's owner? That is not an easy question to answer. If you want to start blog just because you like to blog, I would say no, but if the main purpose of your website is to to get customers for your business or monetize your website in some other way, I would say probably yes, if the asking price is not too high. Godaddy and Sedo are two good places if you want to buy domain from its current owner.