The book of Genesis tells the story of the world. It starts at the very beginning, when "God created the heaven and the earth." The book ends at the death of Joseph, son of Jacob and progenitor of Israel.
Genesis had two very uneven sections in it. The First part of the book, from about chapters 1-11, contains many stories that cover the very first events in human history. First is the story of the first man and woman, where God takes a rib from Adam, the man, and creates from it Eve, a woman. Then the book goes on and tells of the first sin, when Eve was tricked into eating from the tree of the knowledge of good and evil by a serpent. Then it told the story of Cain and Abel and the first murder. Also in the first part was the story of Noah's Ark, where God sent a flood to destroy everything but the immediate family of one man.
The second part of Genesis, chapters 12-50, covers the lives of the progenitors of the Hebrews-Abraham, Isaac, and Jacob. This section takes place over less time than the first 10 chapters.
One thing I noticed in Genesis was that several times, after finishing the story of a certain person, It would say over and over, "so-and-so lived to be so many years old and had this many kids." This made me think that the book of Genesis might have been written less for readability, but more for historical reference.
The purpose of writing Genesis seemed like is to take all things on earth today, link them back to Israel and, ultimately, to God. The way it was done was in a family-tree style. At the top, of the tree would be God. Directly below him would be Adam and Eve, their children, their children, and so on. This would explain the long parts of declaring how long people lived and whom they had as children. I say this because at the time Genesis was written, every major civilization had patriarchs that were descendants of Adam and Eve, according to Genesis.
Because of the whole "linking everything in the world to God" idea that Genesis has, I would say that the target audience would be all Jews, as well as people of other religious backgrounds. I say this because the family tree idea might persuade people of other religions to believe that the Jewish/Christian God is the true god.