There isnīt a complete Shostakovich edition yet. The best option for an inexpensive starter is the
Brilliant Shostakovich Edition of 27 CDs, sometimes available down to perhaps 3 Euros per CD, at least in continental Europe. You get the standard works in decent recordings - the Symphonies with Barshai being very good.
http://www.amazon.com/Shostakovich-E.../dp/B000J20V8K
But Shostakovich wrote a lot, including for instance obscure music for cartoons, an orchestration of Schumannīs Cello Concerto etc., and new manuscripts and revisions also keep turning up - such as the important "Rayok" chamber cantata, or the opera from 1932 "Orango".
The Soviet company Melodiya came close to recording almost everything by the composer and released a lot of rarities, including an LP series "From The Manuscripts Of Different Years" for instance. But they havenīt issued a complete edition yet, and it will no doubt be expensive and very comprehensive too.
However there are usually alternative recordings to the Brilliant set very much worth considering, and as said it is not complete.
One has to make a complete collection step by step anyway ...