The symphonies are tricky, because many of them are wonderful
live but meandering on disc. On disc you should favor 5, 10, 14, and
15. #4 is a breakthrough work but no longer so important. #6-8 are
amazing in concert, with a good conductor, but otherwise a struggle. 9 is pleasant but
slight. #11-13 are a mixed bag, worth knowing, but don’t judge him by
those or start there. For #5 buy Bernstein, for ten buy Mitropoulous or
Mravinsky (though many versions are excellent), for #15 Jarvi or Haitink are good versions. The closing bit of #10 is perhaps my favorite
moment in all of Shostakovich.
Buy the two-disc set of his Preludes and Fugues, Opus 87. Ashkenazy is the version of choice, though I retain a fondness for the idiosyncratic jazzy take of Keith Jarrett. This is the Shostakovich you will enjoy if the sometimes harsh textures of the orchestral works put you off.
Also buy the Op. 67 Trio for Piano, Cello, and Violin, performed by Yo-Yo Ma, Isaac Stern, and Emanuel Ax.
I’ve never been convinced by the opera, the film music, the concerti, the rest of the piano music, or the short jazzy pieces, though all have their defenders.
Here is some summary information.