This is not to say a merchant displaying these characteristics may not go out of business no business is ever guaranteed to stay in business forever.
Based on my experience both marketing online and shopping online I've learned what website characteristics to look for to have confidence in purchasing from any internet merchant or website.
So what attributes do I look for in a website to gain confidence in purchasing online?
First I closely look at the website typically if a website as a quality look and a number of pages with good content is a good sign. Typically if someone is a ripoff they're not going to put a lot of effort into a website just for the purpose of taking advantage of people. It's too much effort for short term gain as word typically travels fast about a disreputable merchant.
Second and this is pretty obvious online merchants that accept American Express (AMEX) are typically in your top tier of merchants. Although the other cards (Visa, MasterCard, Discover) are good AMEX I believe has the best customer service and this makes sense. Those other cards are free, AMEX charges a yearly fee. I like to personally use AMEX when I shop online, they seem to have better service when I might occasionally need it.
Third is the online merchant being part of the BBBOnline (Better Business Bureau) Network. If you don’t see this it doesn't mean they are not a reputable merchant. However, if they do most likely they are.
Other things to look for.
Do they display a telephone number on their website? Are you able to call someone if you have a problem?
On any secure order forms set up to process orders and take credit card information the url address of the page should start with https instead of http. This is the web address shown in the white bar over the top of the webpage.
The bottom line is always use a credit card in shopping online. In the unlikely event you don't get what you pay for you in almost all cases will get all your money back from the credit card company.
The vast majority of merchants online are reputable and reputable merchants like myself always have our eyes open to spot and weed out disreputable websites as they give online business a bad name which is not a good thing for the majority of honest businesses.