As stated previously, as far as technicality and performance go, you cannot go wrong with the Alban Berg Quartett, there are very few quartets they have recorded that have not been done complete justice. The G major quartet, No. 14, from the set is my personal favorite quartet (in general), and is probably the classical piece of which I have listened to the most recordings (I often use this piece as a metric to see if I will enjoy a particular quartet).
Josquin13 has given a very good survey of recordings and I do not disagree with anything they've said; I would use their recommendations as a starting point; however, I would like to vouch for the Takacs recording on Hungaroton, as Josquin said they have not listened. While I usually do not prefer Mozart to be interpreted so freely and loosely, I think No. 14 doesn't suffer nearly as much from this kind of performance as others (the Menuetto suffers the greatest in my opinion, it can drag at times). However, the Andante Cantabile on this record is quite sublime as interpreted by TQ. Plus the recording itself has the most delightful, warm, and intimate quality that's very enchanting. If you're looking for warmth, this recording would suit you, though it is not necessarily my go to/personal favorite.

To add to their list:
Do not sleep on the Casal Quartett recording from 2011 on Telos! (though incomplete, only quartets 14 and 15) I would put this performance right up there with the ABQ. I honestly may even prefer this recording as my favorite of number 14. Their treatment of the material is texturally very delicate and light, but is done with the utmost seriousness, something necessary to convey the true sublimity of this work. I find the recording quality incredibly gentle and refreshing, though the best descriptor may not be "warm" (I do find this recording quite warm, personally), though I would implore you to not let this turn you off of it. While others may perform it with greater technical rigor, no other recording has (for my taste) conveyed the emotional and affective depth of this piece so successfully and immediately. (though some day's I prefer the menuetto slower than CQ take it (it is allegretto, though they take it a little allegro), but their handling of it is still masterful and they do not sacrifice any of the lightness for the speed. This does not detract from the recording at all, simply a reflection of my mood). Do give it a listen:

If you're in the market for digital recordings, I'd give an honorable mention to the Smetana Quartet 2009 recording; Their interpretation is quite nice, though this recording might fail on the 'warmth' front. And, this recording is not a complete set of the six, just 14 and 16.