This summary is drawn from the Rebbe's letters to him (from the 1940s to about 5717, 1957); I did not find a published biography.
Where Providence places you. The Rebbe taught that true spiritual vitality can be achieved even in spiritually challenging surroundings (IK 259), and that wherever Divine Providence places a person is where his unique mission lies (IK 2953).
Constant growth. He encouraged constant growth in Torah and mitzvos without complacency (IK 2036), that every day must be filled with purposeful spiritual activity (IK 4370), and that leadership roles should be used to spread Torah and Chassidus, adapting methods to the audience (IK 2504).
Chassidus. In an early letter the Rebbe explained that true simplicity belongs only to Atzmus, the very Essence of G-d (IK 433).
Sources: the Rebbe's letters cited above.