I recently had the opportunity to read Roger Lewin's Human Evolution, which is an excellent introduction to the adaptations and possible behaviours of some of our immediate ancestors.
Lewin doesn't spend too much time on the long-ago extinct icky creatures you've never heard of; instead, the focus is clearly on primates. Where they came from, what tools they used (if any), how they adapted to new climates (not just from nomadic activity, but also because the earth's climate has cycled a number of times, the last ice age being some 18,000 years ago), and what adaptations moved them closer to who we are today. The adaptations that are most under the spotlight include bipedalism and increased brain size, since these key characteristics separate us from other primates that are still alive today.
The book is meant as an intro and is only some 200 pages, so it may not go into the level of detail of species behaviour that you're looking for. At least, it didn't for me. Instead, a broad top-down view of how primates evolved is provided.
There is also a lot of uncertainty due to gaps in the fossil record and discrepancies in interpreting fossils that have been found. As a result, an inordinate amount of time is spent discussing various possibilities and the evidence for or against various arguments. To do this, the author goes into maybe a little too much detail about dating (not the kind between male and female primates!) and other technologies that are used to interpret the fossil record.
I was looking for a book that linked some of our behaviours to those of our past, and this book does do that to some extent. However, thus far I have not encountered one that does as good a job as Robert Wright's The Moral Animal.