Being that this is for a website, I am not sure as to what kind of information you are looking to post. In this site you will find a list of all the styles of citation that can be used. Academically, MLA and APA are the 2 main ones used, but if this is for technical purposes such as medical or electronic research, they have their own citations. It is hard to tell you which style without knowing the content and context to which the information is being presented, however, the first link should provide you a list with all formats so you can pick which one you would feel is best. If you feel that MLA or APA are the styles you want to use, there are plenty of websites that will generate the citation for you. You just need to enter in the adequate information. A popular site widely used would be CitationMachine.
To answer the main question though, the style isn't related to the place you are writing, but rather the type and style of writing you are trying to do.
commonly online, I have found the quotes to be numbered off with subscript or superscript and then at the bottom associate that number to the reference link. Not sure if that falls under one of those styles but that is just a personal observation of online references used. However, to also point out, there is a difference between references, and citations.