It is well known that the domain names registration has became an industry and some people are making big money from registering or purchasing domain names, developing websites and/or selling or reseling them to others. Beside these people, the main reason of purchasing websites is the someone wants to develop a business or a network of sites and somebody else registered a desired domain name.
It does not matter the reason you are purchasing the website, always check the trends when you are decided to make the step. Even if you are already sure about the domain name you want, the TLD market is always changing, as long the people are pressuring the Internet authorities to release new TLDs. You can always find the free domain names on different TLDs if the primary domain name is already taken. I've head some time ago that there was taken a decision about registering the TLDs freely, as you want, but I'll have to check it out (to update my information) and I'll post another article about this story.
The second issue you must consider is the combination of time, energy and money you can or want to spend on developing the desired website. It may seems cheeper to register a free domain name and to develop the website later than purchasing an existing online website, but it's not always so easy. The Internet is very competitive and developing a brand new site to the point it becomes a concurent to the existing ones can take more money, time and energy you thought it will take at the beginning.
Always check the reputation of the existing domain name and/or the people you are buying the website from. Some times a simple search using yahoo, bing or google is enough to get the necessary data, but usually it's not enough. The online tools can bring additional information about the website: there are chances that the domain was banned or penalized in the past because of malware software or back hat seo methods used to promote it. On the other hand, there are always people trying to scam others with promises they have no intention to put in practice. They do succed in many cases, but the bad reputation precedes them in time and you can spot them if you search enough.
An important thing to consider when purchasing a website is to protect your domain name. It may be possible the previous owner of the site did not protected it (in some ways or not at all), so assure yourself that there is (almost) no chance that you'll get your domain name stolen or redirected to nowhere.
Check the similar domain names of the website you want to purchase. It's possible the one similar domain is more attractive or more succesful than the desired domain.