I heartedly second Swklein's recommendation of recordings by the Mosaiques Quartet. Their Haydn is excellent, as are the recordings by the Kodály Quartet on Naxos.
My recommendations:
HAYDN
String Quartets Op. 76, Nos. 1-6
Kodály Quartet (Naxos)
Mosaïques Quartet (Naive Astrée)
BEETHOVEN
Tokyo or Emerson or Alban Berg Qts
MOZART
String Quartets, K387, K421(Haydn Quartets, disc 1)
Mosaiques Quartet (Naive Astrée)
String Quartets, K464, K465 ("Dissonance") (Haydn Quartets, disc 2)
Mosaiques Quartet (Naive Astrée)
My recommendations:
HAYDN
String Quartets Op. 76, Nos. 1-6
Kodály Quartet (Naxos)
Mosaïques Quartet (Naive Astrée)
BEETHOVEN
Tokyo or Emerson or Alban Berg Qts
MOZART
String Quartets, K387, K421(Haydn Quartets, disc 1)
Mosaiques Quartet (Naive Astrée)
String Quartets, K464, K465 ("Dissonance") (Haydn Quartets, disc 2)
Mosaiques Quartet (Naive Astrée)