We have lots of recommendations on our book list and, since you're also interested in anthropology, so does /r/AskAnthropology.

I found Jared Diamonds Guns, Germs and Steel to be an excellent read: it gives a broad introduction to the development of early human societies. I know a lot of people disagree with his works though - but I'd still give it a read - its accessible but quite broad in its scope.

What's with the down votes? OP asked for a book recommendation for someone that knows very little about early homosapiens. If there are better books on the subject I'd like to read them myself.