There are a lot of testing methods out there i.e. blackbox, graybox, unit, functional, regression etc.
Obviously, a project cannot take on all testing methods. So
Well before going to the answer i would like to clear testing concept about multiple methods.
There are six main testing types which cover all most all testing methods.
Almost all Testing methods lies under these types, you can also use some testing method in multiple types like you can use Smoke testing in black box or white box approach on the basis of resources available to test.
So for testing a web site completely you need to use at least following testing methods on the basis of resources available to test. These are at least methods which should be used to test a web site, but there may be some more imp methods on the basic of nature of website.
You should at least use all of above (8) testing methods to test a web site no matter what testing type you are focusing. You can automate you test in some areas and you can do this manually it all depends upon the resources availability.
There is specifically no hard and fast rule to follow any testing type or any method. As you know "Testing Is An ART" so art don't have rules or boundaries. Its totally up to you What you use to test and how.......
Hope you got the answer of question.