Learning grammar rules by reading a grammar book is not a very effective way of learning to use grammar correctly. It is more effective to constantly keep track of the grammatical constructions you are using (or encountering), tracking where you make mistakes and then to practise and improve specifically those constructions.
It is also helpful to find a grammar practice book that contains a self test and an answer key and that refers you to specific sections in the book for the answers you got wrong. How English Works: A Grammar Practice Book by Michael Swan and Catherine Walter (Oxford University Press, 1997) is such a book, which has sadly gone out of print, but which may still be found in second-hand book shops and libraries. It has a self test at the beginning at the book. The bulk of the book contains sections with grammatical explanations followed by exercises, beginning with a two sections on determiners and ending with sections on relative clauses and prepositions. (The explanations are short. For more detailed explanations, the authors refer to Practical English Usage by Michael Swan.)
The excellent book English Grammar in Use by Raymond Murphy (Cambridge University Press, now in its fourth edition) has something similar. My copy of the second edition (1994) has a section entitled "Study Guide" near the end of the book, which is meant to help you decide which units to study by means of a series of exercises (9 pages, without counting the answer key). In this book, grammatical aspects are taught in a different order than in How English Works. For example, the first three units focus on tenses, and the unit on articles and nouns comes after those on verbs. Other books in the same series include Essential Grammar in Use (for CEFR levels A1-B1) and Advanced Grammar in Use (for CEFR levels C1-C2).
There are many different ways of organising a grammar book. For example, A University Grammar of English by Randolph Quirk and Sidney Greenbaum (Longman, 1973) begins with chapters on (1) Varieties of English, (2) Elements of grammar, (3) Verbs and the verb phrase and (4) Nouns, pronouns, and the basic noun phrase, and end with chapters on (11) The complex sentence, (12) The verb and its complementation, (13) The complex noun phrase and (14) Focus, theme, and emphasis. This type of grammar of you want to be learn the rules themselves rather than learning to use the rules. (At university, I studied a book like this; at the oral exam, I was asked questions such as, "Explain the usage of the subjunctive".) If you want to learn correct grammar from a book like this, you would need to turn the example sentences into exercises (e.g. fill-in-the-blank exercises) and find additional examples elsewhere.
A Communicative Grammar of English by Geoffrey Leech and Jan Svartvik (second edition, Longman, 1994) takes a different approach. Part One is "A guide to the use of this book" (35 pages!), Part Two contains four thematic sections: (A) "Concepts" (e.g. objects, concrete versus abstract, quantity, time, degree), (B) "Information, reality and belief", (C) "Mood, emotion and attitude" and (D) Meanings and connected discourse". This part fills roughly 180 pages. Part Three is an "A-Z in English Grammar". Whereas Quirk and Greenbaum used a structural approach, this book uses a communicative approach. The book's introduction discusses the rationale behind this organisation:
[In a conventional grammar, for example], notions of time may be dealt with is as many as four different places: under the tense of the verb, under time adverbs, under prepositional phrases denoting time, and under temporal conjunctions and clauses. The student who is primarily interested in making use of the language rather than in learning about its structure (and this is true for the majority of foreign students) is not likely to find such an arrangement particularly helpful.
The most detailed English grammar I own is Cambridge Grammar of English: A Comprehensive Guide by Ronald Carter and Michael McCarthy (Cambridge University Press, 2006; 973 pages). This is also organised in what Leec and Svartvik called the "structural approach" and it serves mostly as a reference work. If you wanted to learn to use correct grammar from this book, you would need to turn the example sentences into exercises (and find additional example sentences elsewhere). See my answer to Is it possible to learn grammar through spaced repetition, and if yes, how? for a suggested method.
Conclusion: there is no single "best" order to revised the aspects of English grammar. Conventional grammars that use a structural approach don't always use the same order. Grammars for learners of English also use different ways to structure the material. For this reason, my advice is to focus first on those areas where you experience difficulties, by using a self test (see the first two books I suggested), by tracking the types of mistakes in your own spoken or written language, or both. After that, you can still learn other aspects of grammar.
