If you're looking for a book that will serve as an excellent companion for your reading of Capital: Volume 1: A Critique of Political Economy (Penguin Classics), then this book is what you want. It's a clear, engaging text by an author who is perhaps the greatest living Marxist scholar. It fulfills the role of a companion book almost perfectly.
Capital is a book that people should be reading right now. Whether or not you consider yourself to be a Marxist, it is critical that academics, students, and laymen start to question the basics of the mainstream narrative of global capitalism. Capital may have been written 150 years ago, but its content is frighteningly relevant. On a purely practical level, Harvey's companion will help you overcome some of the seemingly anachronistic areas of Capital, such as the detailed analyses of the history of 19th century class struggle, Marx's account of primitive accumulation at the end of Vol. 1, and Marx's reliance on the standard British industrial factory of his time as a model of capitalist social relations. Throughout the companion, Harvey explains Marx's various reasons for using the pieces of evidence that he did when constructing his arguments, thus also demonstrating that Marx's arguments are still perfectly applicable in the modern world, even if there have been significant historical and economic changes since Marx's time. By doing this, Harvey not only proves the continued relevance of Capital, but also eliminates and illusions of anachronicity from the reader's experience with Capital.
Harvey provides many insightful observations about the operation of the Labor Theory of Value, class conflict, and exploitation in the modern global economy, which helps the reader further understand that Marx's critique is a critique of the capitalism we experience as much as it is a critique of the capitalism of his own era. Part of the Marxian understanding of capitalism is that capital constantly operates according to certain laws and contradictions that are mandated by capitalist social relations. One of the biggest obstacles I personally find when arguing about capitalism with my peers is the perception that the social relations and contradictions that Marx identified only applied to a certain period of capitalist development, not the capitalism in its entirety. Harvey helps readers of Capital realize that this isn't the case at all, and that there are no signs that capitalism is ever going to overcome its own contradictions by itself.
Aside from these more tangible benefits, I also find "Harvey's" Marxism to be a productive perspective to explore Marx's work through. Although Harvey claims that he is trying to help the reader "read Capital on Marx's own terms," it is obviously true that the reader is inevitably receiving Harvey's own Marxism (which Harvey admits to at various points) in the companion. Harvey's interpretation of Capital heavily emphasizes dialectics as an approach to social science. Harvey is skeptical of anybody who sees the totality of social relations as "caused" by some particular factor, and he is critical of people who try to describe Marx's writings through causal language. In turn, Harvey proposes that there are seven different spheres that are inherent to any society, and that the qualities of one sphere depend on the qualities of the others. These sphere include the mode of political organization, the relation to nature, the society's phenomenology of time, culture, and others. The ways in which these spheres interact are not obvious for all to see. Painstaking research and observation is required in order to properly comprehend these relations. Harvey never passes up a chance to show how Marx knew this as well, and as a result, Harvey forges a tight group of arguments in favor for his own interpretations of Marxian social theory and economics.
When I say that Harvey's lens works well for beginning readers of Marx, I make this claim because Marx vis-à-vis Harvey is very much open to input from multiple perspectives. In reading both Capital and this companion, I found myself referring back to German phenomenology, political theory, and the history of colonialism. This is probably because I have a halfway decent background in these subjects. However, Harvey frequently invites the reader to keep historical, anthropological, philosophical, cultural, and economic perspectives in mind when reading Capital, and to grapple with the question of how these different perspectives are inherently interrelated. His open-minded reading of Capital helped bring out my own sense of intellectual curiosity.
As a quick note, Id' also like to say that this companion isn't just for first-time readers of Capital (although that's precisely what I was when reading it!) This companion, as far as I can tell, contains the best collection of arguments in favor of Harvey's own heavily dialectical interpretation of Marx and his criticisms of rival interpretations. Then again, I'm still reading The Limits to Capital (New and updated edition), so I may be wrong here.