Study the book "Computer Architecture- A quantitative approach" (3rd Edition) for the first time
I think you first need to decide what your goals are. Are you interested in computer architecture because:


You want to design computer hardware and so need to understand it at a fundamental level?
Or because you want to write software whose performance is enhanced by an above-average understanding of computer architecture?
Or because you are just mildly curious about how computer architecture works?


In the preface to the 3rd addition, the authors talk about why they selected the material they did, and they give this warning:


  To allow for this new material, we reduced the extent of introductory material, assuming the knowledge of the concepts in our introductory text, Computer Organization and Design: The Hardware/Software Interface.


So my advice is to start with that introductory text. If all you're interested in is a passing understanding of how the architecture works so you can write better software, or because you're just curious, then you can probably stop at that point.

The introductory text (at least the 4th edition of it) also includes a chart at the beginning listing which sections of the book should be read for a hardware focus or software focus, which should be read carefully, which can be glossed over, and which are just interesting but not necessary.

If you really want to understand modern computer architecture at a fundamental level, then after finishing the introductory text, you should probably get a later edition of the advanced text.

The fourth edition added coverage of multicore chips, which is a pretty fundamental aspect of modern computer hardware. The fifth edition has some pretty significant changes and adds an emphasis on mobile device architecture. 

As for what order to cover the chapters, each edition is a bit different, but the the preface of each one contains suggested reading paths depending on what your goals are. The later editions go into more detail on this (by section rather than by chapter).