The Selfish Gene should be read by everyone who studies biology or life science. Modern biological sciences are underlied by an understanding of evolution an genetics. I had heard variants of the phrase "change in allele frequency in a population over time," as a description of evolution many times starting in high school. But it wasn't until I read The Selfish Gene in college that I really understood what this meant…
Indeed. We are only vessels for our genes, what we do doesn't really matter as long as we pass our genes along, from the perspective of our genes. I would also recommend other Dawkins books such as The God Delusion, it was one of the pivotal books that turned me from someone vaguely religious to an atheist. It explains simply how the various fallacies of religions are explainable and unwrappable.
I think this only sells it to other people who are vaguely religious and are looking to be atheist.