Mozart,Haydn,Beethoven String Quartets......

You can't go wrong, although tastes will vary, with recordings by the Tokyo, Emerson, or Alban Berg quartets of this repertoire in the digital era; some like the Lindsays a lot (particularly British listeners) in Haydn. For period performances of Mozart and Haydn, you could try the excellent Quatour Mosaiques. If you can get over the need for digital recordings, the best performances bar none IMO are the Vegh for the Beethoven, and the Tatrai for Haydn. I also like the Quartetto Italiano in Mozart. For Haydn, don't bother with the generally critically lauded Kodaly performances on Naxos, an admittedly attractive budget alternative-- they just aren't that good, and aren't a patch on the older Tatrai.

The Borodin by Borodin are indeed spectacular. For "Death and the Maiden" there are excellent recordings by the Emerson and Tokyo, and the best of all is the Busch Quartet from the 1930s (which can be found, or could once, on EMI/Angel CD: don't sweat the dated sound, it's surprisingly vivid). You might want to try the Brahms quartets (Alban Berg, Takacs are good), the Bartok (Tokyo, Emerson, best of all Vegh), the Janacek (Tokyo, Smetana). These are some of m favorites!

Of course! The Dvoraks! Hard to play them badly, recorded evidence suggests. I have a soft spot for the Chilingirian Quartet on Chandos: excellent performances of the major quartets, with smooth and rich sound. Don't miss the G major quartet: it's the best, despite the far greater name recognition of the "American"...