This review is a sort of reader's guide to "The Complete Works". I've grouped Aristotle's works into logically related sets, provided a list of the works for each set (in the recommended reading order), and also indicated what sets are prior reading for which other sets. Note that I've restricted myself to those works of undoubted authenticity.
To use this review, locate the set containing a work you are interested in, read the sets that are logically prior to it, and then the prior works in that set.
Categories
"Categories" - Is it about words, ideas, or metaphysics? The answer is: yes! This is the most foundational of Aristotle's works. For almost anything of Aristotle's you plan to read, you should read this first.
Logic
"De Interpretatione", "Prior Analytics", "Posterior Analytics", "Topics", "Sophistical Refutations" - "Categories"is a prerequisite. "De Interpretatione" is about statements (and negations), "Prior Analytics" is about deductions, "Posterior Analytics" is about demonstrations, and "Topics" is about dialectical deduction (and proper formation of definitions). "Sophistical Refutations" is really an appendix to "Topics" and deals with various logical fallacies. Mostly, they're not difficult reading, but "Prior Analytics" may have been the most numbing thing I've read in my whole life. The material about definitions in "Topics" has profound importance for Aristotle's metaphysics.
General Science
"Physics", "On the Heavens", "On Generation and Corruption", "Meteorology" - "Categories" is a prerequisite, and the Logic set is recommended prior reading. "Physics" concerns change - the words "motion", "movement", and so on are often used to indicate any kind of change, not just a change in location. "On the Heavens" concerns cosmology. "On Generation and Corruption" is broadly about chemistry. "Meteorology" is about atmospheric phenomena, but includes such things as comets and earthquakes. Aristotelian physics and cosmology, though pretty thoroughly wrong, have a coherence that goes far to account for their longevity. His equivalent to chemistry, on the other hand, is not only pretty thoroughly wrong, but wrong in ways that really, really make you wish that Aristotle had been willing to say "I don't know" a lot more often than he was.
Biology
"On the Soul", "Sense and Sensibilia", "On Memory", "On Sleep", "On Dreams", "On Divination in Sleep", "On Length and Shortness of Life", "On Youth, Old Age, Life and Death, and Respiration", "Movement of Animals" - "Categories" and the General Science set are prerequisites. "Soul" is a word with a great many associations with Christian belief that should be forgotten before reading this set of works; for Aristotle, in this context, "soul" in this context pretty much means the qualities of living things that differentiate them from non-living and he builds up from there. The titles of these are largely self-explanatory. The bad chemistry in "On Generation and Corruption" leads to even worse biology here.
Zoology
"History of Animals", "Parts of Animals", "Progression of Animals", "Generation of Animals" - "Categories", the General Science set, and the Biology set are prerequisites. Aristotle's writings on Zoology are a farrago of careful observation, folklore, and tall tales. Generally, when people want to make fun of Aristotle, they look in these works for quotes. I will resist the temptation to quote any of them here, and just point out that in Aristotle's time, the technical and social means for doing good work in this area just didn't exist.
Metaphysics
"Metaphysics" - "Categories", the Logic set, and the General Science set are prerequisites, with the Biology set recommended, but not necessary. Although "Metaphysics" is famously difficult, you may not find it too hard if you have read the recommended prior works (particularly the material on definitions in "Topics"), and don't get too obsessed about trying to understand his attempts at refuting the views of philosophers whose works we no longer possess. Also, be aware that there are some confusing uses of the word "soul" as well that pretty clearly have a much broader meaning than those in the set on Biology.
Ethics
"Eudemian Ethics", "Nicomachean Ethics" - No prerequisites. Both of these are lecture notes taken by students, whose names grace the titles of the works. The works are overlapping and don't have a real logical order. Of the two, Nicomachean Ethics is longer and covers more ground, and is therefore more commonly referenced than Eudemian Ethics, but the Eudemian Ethics flows better, and is the better one to read first. Some historical background reading about Greek society at this time is recommended. Perhaps surprisingly, after reading Aristotle's Ethics, his "Rhetoric" is highly recommended follow-up reading (the dark side of ethics, so to speak).
Politics
"Constitution of Athens", "Politics" - The Ethics set is a prerequisite. "Constitution of Athens" is a political history of Athens. "Politics" is political theory. Reading "Constitution of Athens" before "Politics" can help provide context for the latter work, although additional historical background reading about Greece in Aristotle's time is highly recommended.
Rhetoric
"Rhetoric" - "Categories", the Logic set, and the Ethics set are recommended prior reading. "Rhetoric" was a somewhat disreputable subject for Aristotle in that it aimed not at knowledge, but at persuasion, and by any means fair or foul. As part of this work, Aristotle expounds quite a bit on human nature, which makes this a fascinating follow-on to his works on Ethics.
Aesthetics
"Poetics" - No real prerequisites. This work, though short, has profoundly impacted aesthetic theory, particularly in the dramatic arts. Everyone should read this.