My quick reccomends, besides the Beethoven Qts (of course) and Debussy Qt
(oh my god) are

Shostakovich: Almost every of the 15 are great, I have the complete set by
the Borodin Qt

and newly:

Peter Maxwell Davis: String Quartet--very interesting, short early English
Avant-Garde noise from the 60s.

Also, my favorite Debussy Qt currently is by the Rubin Qt, a little-known
all-female Qt from eastern Europe somewhere, on a little label called New
Classic Colours.

Enjoy.

Bob K.