Hi Ryman. I think the most common (and the one I use) is an immersion chiller. Its advantage is that its easy to make (if you want to make your own) and relatively inexpensive. In my experience, it gets the job done with minimal fuss.
Some folks use an entire brewing system where they are pumping wort through their system. For that kind of setup, one of the other options where you are pumping your wort through the chiller makes a lot of sense. I think both plate and counterflow chillers also have the potential of cooling your wort faster than an immersion chiller.
For a basic setup, I recommend an immersion chiller for getting the job done easily and without any hassle.