I use the Borodin (original members) version because they're the ones I know best. I'm sure alternative versions, or the Beethoven or Bartok string quartets, would also do the job, possibly better.
One strike against this set is that most or possibly all of the CDs have been produced from LPs. Having bought the vinyl versions (twice!) many decades ago, this is good for me but not so good for you.
http://www.amazon.co.uk/Shostakovich-String-Quartets-1-13-D/...
One thing about newer recordings is that they may well be closer-miked and not have such a "natural" sound stage.
Any particular recording you would advise? I mean a specific record of known-good quality, preferably on iTunes, Amazon, or similar. I often find myself spending a lot of time listening to different records of the same piece, just to make sure I get a good one.