Are halogens a further classification of non-metals, or are they another group themselves?
Halogens are merely just a subset of non-metals. Consider this periodic table:



Clearly halogens do come under the fluoroscent colored elements, which signifies non-metals. There are several other groups, which have their own unique name. For instance, the oxygen group members are called chalcogens, and the nitrogen group members are called pnictogens.

However, there is something special about halogens though. They are infact the most non-metallic elements known, considering their great tendency to gain electrons. This also makes the halogen group the only group other than inert gases to have only non metals in them (ignoring Ununseptium of course).

In short, halogens are a subset of non-metals and not an entire class by themselves. But they are, the most important subset of non metals.