I would recommend Arvo Pärt as well. I have around 15 of his albums and I think I would say he is probably my favorite composer of all time. His masterpieces are unparalleled in their divine beauty. Having started teaching myself to play the piano recently, I even have the sheet music for three of his works: Für Alina, Spiegel im Spiegel, and Variationen zur Gesundung von Arinuschka. The best starting point for any unfamiliar with his work would definitely be the album Tabula Rasa on ECM. The only thing it lacks is an example of Pärt's sublime choral works. For that there are several great albums out there. Kanon pokajanen is my personal favorite, but it might be a bit too large a work as a first introduction.
Arvo Part is one of my favourite composers. One of the latest of my favourite composers ("mystic minimalists") is Pēteris Vasks, you could find most popular of his works in youtube.