the early quartets (op 18) are fairly non-exciting, although they are still pretty good. The Rasumovsky quartets (op 59) are amazing. I think Op 59 No 3 is one of the best quartets ever, especially mvt 2 (andantino quasi allegretto) which is the work of an absolute musical genius of the highest order. The rest of the middle quartets (the other two in Op 59 plus Op 74 and Op 95) are also good. The late quartets are all amazing. My favorites are Op 130 (which originally had as the finale the Great Fugue, although it was later pulled out as a standalone piece and a new shorter finale inserted) along with the Great Fugue and also Op 131 is quite awesome.

but absolutely listen to Op 59 No 3 (all of it, although most especially mvt 2). It might be more special to me because I wrote a significant analysis of the second movement, but more likely I wrote the analysis because it was so special.