What are the high school clicks that Melinda names? Which ones are important to Speak? Why?

The answer to your question can be found within the first few pages of the novel.  Melinda has entered the Merryweather High auditorium for what seems to be the first assembly of the school year.  Melinda immediately notices all of, what she calls, the high school "clans."

We fall into clans:  Jocks, Country Clubbers, Idiot Savants, Cheerleaders, Human Waste, Eurotrash, Future Fascists of America, Big Hair Chix, the Marthas, Suffering Artists, Thespians, Goths, Shredders.  I am clanless. (4)

Melinda goes on to explain that her old clan the "Plain Janes" has "splintered," with its members being absorbed by other clans above.  It is this statement that makes a few of these clans quite significant (even the one that is now extinct):

PLAIN JANES:  There are probably other members of this group, but the main ones were Melinda, Rachel, Ivy, Nicole, and Jessica (who has since moved to Nevada).  Obviously, their name suggests that there was nothing incredibly special about them as a group:  average looking girls doing average things.  That has changed.

JOCKS:  This clan is significant because it has absorbed Melinda's "ex-friend" Nicole.  Nicole has always been athletic and shows lots of promise in the sports arena so she spends the beginning of school "comparing scars from summer league sports" (4).

EUROTRASH:  Melinda doesn't shift Rachel into this group quite yet, but it becomes clearer as the novel flows.  Rachel begins to be known as Rachel/Rachelle, hanging with all of the foreign exchange students.  At this first assembly, Melinda something a bit simpler.

It's Rachel, surrounded by a bunch of kids wearing clothes that most definitely did not come from the EastSide Mall. (4)

MARTHAS:  This clan is important because it is the precice one that her new "friend" named Heather tries to join.  They are the ones who always wear matching clothes with accessories and do volunteer work day and night.

SUFFERING ARTISTS & THESPIANS:  This is the group that has absorbed Ivy.  Melinda says that "she has enough personality to travel with two packs" (4).  In my opinion, it Ivy with her art experience that truly breaks the ice again with Melinda at the mall, chapters later.