You can never have enough method books as a trumpet player. There may be many books about the same things like buzzing, long tones, articulation, lip flexibility, and more. However, each book has it's own unique take on the subjects and offer different ideas for your practice. Money is limited, but when you have the time I suggest you add these books to your collection if you haven't already. I will list some of the books I think are essential to beginning and intermediate students. If you click the images the link will send you to an external webpage where you can purchase the book. A quick tip for music buying, Amazon is always great, it's also faster and great to support local if you have a music store near you. However, if the books are not in stock, look around first. Music publishers have been pretty slow over the past few years, if the book is out of stock it could take months for them to get another in stock.
Essential Books For Beginner Students
H. L. Clarke - Technical Studies for the Cornet
This book is the first book I ask my students to get after they get their band method book. I use the Clarke method to first introduce all of the notes and fingerings on the trumpet in the first study, then use the other studies to help students gain a deeper understanding of their major and minor scales. Once the exercises have been mastered we begin adding different focuses such as dynamics, articulations, and tempos to create new challenges.
Earl D. Irons - Twenty-Seven Groups of Exercises for Cornet and Trumpet
This is another essential as a beginner. When we start learning to play the trumpet, one of the things we need to understand right away is where all the different partials are on the instrument. The Irons does a great job taking you through all the different notes you can play with just one fingering. I find this book helps students gain a better understanding of where each of the notes are on the trumpet.
Robert W. Getchell - First Book of Practical Studies for Cornet and Trumpet
This is a wonderful etude book for beginners to bring everything together. Getchell does a great job introducing simple melodies, while continuing to add new elements like dynamics, tempo, and key signatures to keep you on your toes. For some of my more advanced students I would maybe recommend you get the Second Book of Practical Studies. I still use this book today to practice piccolo trumpet.
Essential Books for Intermediate Students
Jean Baptiste Arban - Complete Conservatory Method for Trumpet
The "Trumpet Bible" as many call it is an essential to any intermediate player. This book takes you through just about every technique you would need to know to play the trumpet proficiently. It has long tones, articulation, multiple articulation, lip flexibilities, trills, grace notes, range, lyrical etudes, technical etudes, solos and duets. There really isn't anything this book doesn't have. I mostly use the Arban book for articulation, etudes, solos and duets.
Wiff Rudd - Collaborative Practice Concepts for Trumpet
I'm currently in love with everything about this book. It's one of the few books I have actually read the text in. Wiff starts with an excellent warmup routine that can be played alone or with others. Wiff mixes many different approaches and methods into his very own book. I always feel like a million bucks after warming up to this method. Plus Wiff usually writes a personal message when you order the book from him which is really cool.
Phil Snedecor - Lyrical Etudes for Trumpet
This book is an excellent etude book for an intermediate trumpet player. The etudes aren't extremely technical, and many of them don't go too high into the upper register. I enjoy using this book for phrasing, performance practice, and endurance.
J. L. Small - Twenty-Seven Melodious and Rhythmic Exercises for Trumpet
These etudes are so much fun to play. Each etude does a great job with mixing satisfying musical sections and challenging technical areas. They are the perfect length, and always fun to revisit.