It can be rather difficult to decide on the "most important" events in a given work of literature, but here goes. You might want to re-read the novel and see if you agree or disagree with my choice of events, as certainly this is a great book with many different plot elements.
Firstly, quite clearly we need to start with Sam Gribley's exit from the hustling, bustling city and his move to the far more tranquil countryside. His first night and its various disasters is interesting in terms of providing a marker to show how quickly he learns and develops the skills and strategies necessary to survive. The first night, for example, he is even unable to start a fire.
Secondly, I would select the stage in the novel when Sam has his own home in his tree and has worked out how to sustain his life and is hoarding for the winter. This clearly is an important section of the novel because it shows how Sam has mastered all the necessary skills for survival in his chosen location.
Finally, I would select the time when a variety of newspaper reports are published about Sam, as it represents the beginning of the end for his solitary life, culminating in the arrival of his family to live with him.