For me, Shostakovich's most compelling symphonies are the First, Fourth, Fifth, Eighth, Tenth, Thirteenth, and Fifteenth. However, I wouldn't focus on the Thirteenth and Fifteenth until you've absorbed the earlier symphonies.
In terms of conductors, along with Rozhdestvensky and Kondrashin, I would also recommend Barshai & Mravinsky.
I also enjoy Haitink and Ormandy in DSCH -- even though (at times) their sounds aren't as idiomatic as Russian orchestras under Russian conductors. That said, for example, Haitink's Eighth is AMAZING. (I like it even better than Mravinsky's famous version of the 8th.) And Ormandy's Tenth is outstanding too. (Philadelphia actually has a tradition of performing Russian music, and Ormandy gave the American premieres of several DSCH works.)
I like to think of Shostakovich as Mahler's heir. They have quite a bit in common, and DSCH loved Mahler's music -- especially Das Lied von der Erde. Of course, the circumstances of DSCH's life were very different than Mahler's, and understanding the particulars of DSCH's life in the Soviet Union is a critically important part of fully understanding his music.
EDIT
I watched this DSCH lecture recently and enjoyed it very much. Well worth a look.