Can't speak for chlorine, never tested it. API makes a pretty good hobby level kit for ammonia, nitrite, nitrate, and pH. Realistically, in an aquarium, those are the only things you need to test. Of course, there are exceptions like gh and kh, then iron, phosphates, etc... But those are what I would consider 'specialty' or purpose driven tests.
Just curious, why are you wanting to test chlorine?