Which of Rav Kook's books would be the one to learn if you want to see his learning style and methodology. What I mean is, in which book does he most "show his work" so to speak.
You probably will want to start with Orot. R Bezalel Naor recently came out with a very nice English translation including an extensive historical introduction and notes.
However, be warned that this is a very difficult text to learn alone. The style is very poetic and there are many references to concepts which are not explicit in the text. I learned it with a specialist of R Kook and realized I would not have understood 10% on my own. Audio shiurim going through the text might be a worthwhile alternative.
Another book which helps get into R Kook's works is The Essential Writings of Abraham Isaac Kook by R Ben Zion Bokser which includes selections of various works incl. Orot of course.