ChamberNut,
I'd recommend that you buy the entire ballet. Why settle for snippets? The whole piece is so extravagantly beautiful. And there are several good recordings. Kitayenko, Gergiev, Ozawa, Previn, Maazel, Mogrelia. I grew up on Leinsdorf's recording of excerpts, and Maazel's was the first recording I had of the complete ballet. It's very fine, but I probably listen to Previn or Gergiev most often nowadays. The Mogrelia is surprisingly good--real scrappy, though--and has the additional advantage of being on Naxos.
Otherwise, I was surprised to see Prokofiev described in this thread as the introvert and Shostakovich as the extrovert as that's the opposite of what most commentators have said. I would say that both views are wrong as too limiting. Both of those composers were great composers, so they both cover a wide range of musical meaning. Prokofiev covered the wider range, I'd say, but almost all my Russian friends prefer Shostakovich. Prokofiev's too "cool" and "acerbic" for their tastes, I suppose, though he's so much more than those two words imply.
As for the piano concertos, they're all great, except for maybe the first one, which is often kind of silly. But it's such an engaging silliness, it's difficult not to love it. The fifth is the least well liked, for some reason. It's practically the most perfect thing Prokofiev wrote, that and the Quintet and the eighth piano sonata. Which is saying a lot, as the quality of Prokofiev's music is pretty uniformly high. It's not immediately engaging, a lot of it, which is why only a few works seem to be well-known. Give it time, and you'll see how rich and various it all is.
And don't forget those operas, either. Eight of them, and at least four of those among the finest operas ever. At least. (Love for Three Oranges, Semyon Kotko, Betrothal in a Monastery, and War and Peace. Which is not to say that Maddelena and The Gambler and The Fiery Angel aren't well worth a listen. I don't know about The Story of a Real Man, yet, as the only recording is of a truncated version of the truncated version. Yes, you read right.)