Litany is such an effective and profound piece. The two works for string orchestra that follow it on the ECM recording, Psalom and Trisagion, are very somber pieces and easily make that my favorite recording of Part.
Gidon Kremer's recording of Fratres and Tabula Rasa on ECM are classic. Gil Shaham's recording of the version of Fratres for violin, percussion and string orchestra on Deutsche Grammaphon is less bleak and a little more romantic, but it's also very notable. On the same DG cd, there are also recordings of Tabula Rasa and Symphony no.3. Both are pretty good, but the Gidon Kremer recording of Tabula Rasa is on another level. Symphony no.3 was composed prior to the transition in Part's music in the mid 70s and is of a rather different (and perhaps less spiritual) character than the other works but it is enjoyable. I would certainly recommend this DG recording over the Naxos one.
Those who want even more minimalistic pieces could check out the ECM recording titled Alina which has three slightly different recordings of Für Alina and two recordings of Spiegel im Spiegel.
Part has become more popular than other contemporary composers, perhaps due to the fact that his music from the 70s on has been less demanding on the listener than others'. But I could see someone getting into Part and Gorecki first and then going on to check out other contemporary composers such as Penderecki, Schnittke, Ligeti and Reich.