Unfortunately, I can't really offer you specific rules from a music theory standpoint, as the style itself is still somewhat incipient. However, as I'm sure you already know, it is based on the repetition and slight variation of a specific motif. The motif is generally stated simply early on in the piece and then repeats extensively throughout, undergoing slight modification during the development section. From my experience with the genre (mainly the works of Phillip Glass and John Adams) the piece can have a formal coda or simply come to a stop. I, too, have become a fan of this style and have written several pieces in it, though I remain a Romanticist at heart
I strongly encourage you to listen to the two above mentioned composers (Glass and Adams) to enhance your understanding of the genre in a very modern context, as both of them are still alive and working on new pieces. Though arguable, some would consider Shostakovich a minimalist composer, yet in a far less strict sense than most modern composers of the same ilk.
I believe it is certainly a worthy endeavor as a composer of classical music to become educated and familiar with this contemporary style, regardless of whether one chooses to embrace it, as it is presently en vogue and ostensibly the future direction of "formal music" in general.
The best way to learn, as with most things, is by doing. Write a few pieces in the style to the best of your ability and go from there. Regarding specific intervals, I would suggests you keep your harmony "open" if you're looking to achieve a modern sound, that is, use fourths and fifths of the tonic with no third---the use of a third is a very conventional practice and, consequently, makes for a traditional sound. Seventh and ninth chords sound more "jazzy" or Debussy than minimalist, but you should really just experiment and see what appeals to your ear.
Good luck and best regards for the future!