Cantonese is a rewarding but demanding target for the English speaker. It is strongly tonal, its everyday spoken form differs from written standard Chinese, and good learner materials are scarcer than for Mandarin. That makes a sensible book order especially valuable, so you are not jumping between mismatched romanization systems and levels.
An honest caveat: books can build your grammar, vocabulary and reading, but Cantonese tones and natural speech require active listening and speaking practice. Pair every book with audio, and speak aloud from day one, or the tones will not become automatic.
Get grounded
Start with Cantonese, a clear grammar-and-usage introduction that lays out how the language actually works. Then Colloquial Cantonese is a full beginner course with audio, focused on the practical spoken language you will really use. Reading them together gives you both the map of the grammar and a working set of everyday phrases.
Characters and structure
Because the writing system is a mountain, tackle it deliberately. Remembering simplified Hanzi gives a memory-based method for learning characters, which is more efficient than rote copying, while A Cantonese Book supports your study of the language's own conventions. Here the reading-versus-speaking split is sharpest: characters are pure book work, but keep drilling the spoken side in parallel so the two reinforce each other.
Build toward fluency
Now climb the levels. Basic Cantonese and Intermediate Cantonese form a paired grammar course that walks you systematically from foundations to more complex structures, an ideal spine for steady progress. Cantonese for Everyone broadens your practical vocabulary and situations, and Easy Cantonese offers a light phrasebook-style resource for quick reference and travel. Working up through these in order keeps each step within reach of the last.
Follow the full path in sequence, always with audio and spoken practice, and Cantonese becomes far more approachable.