First thing to do is to make a list of what you want to do with your website. Then look at the fully-built websites. Tick off your checklist. After that, look at the price. Then compare the price to what you would have to pay if you were to build the website yourself.
First of all you need to do some market research to see if similar sites that sell same sort of products and services are making good money and if still there is any opportunity to make money out of it. You need to check some statistics such as popularity and traffic and unique visitors per day and compare that figures with other competitive sites using some online statistics tools such as Alexa.
I agree with Sarleons, you're going to want to see if there's other better deals, or websites with better features. Really try to look at what features you think the site offers that are going to appeal to clients / customers in a way that its peers currently don't. Secondly, is the website something you're very confident will still be relevant years down the road? The best investment is a website that's not just hot and new with fad features, but something that's got a timeless theme, but the new coding to give it an edge over what's already available.
You would want to consider the popularity of the site. If the site has been up for a while and has a fan base then you can take advantage of the traffic. I would like to know what type of audience the site attracted before. For example, if the site was a gaming site and you wanted to sell a vegan cook book then the traffic doesn't do much good. One way to does this is to go to archive.org and put in the web domain. One thing you should always remembers is traffic is king. If it is a site that has authority or good traffic then that means that you could potentially make good money selling something on it.
also - don't forget, and this is important - do they have positive seller ratings and a verified paypal account? If it's a new seller with no ratings and they sound even 1% shady, then don't deal with them. Go with someone that offers a sense of trust.
Before you buy a website, check the following things:
Traffic: How many visitors the website gets in a day, what is the location of the visitors, what is the bounce rate?
Advertising: Which ad network does the website use? Is there Google Adsense? You must be aware that most of the ad network accounts are non transferable, which means you will not earn from advertising on the website.
1. Does the niche interest you at all? Because you will be continuing the site and you need to have some knowledge about the niche of that site.
2. Is it a relevant niche? Is the owner selling the site because it's not relevant anymore or simply because he's tired of it?
3. Does it get a considerable amount of visitors? Does the site already have a following that's worth its price?
In the end, it's still your choice but you have to think of these factors as much as you can. Good luck!