Reddit reviews Venture Brass Mouthpiece Brush

Mouthpieces don't wear out (they are solid metal). Give it a good wash and scrape inside with a mouthpiece brush. If the bottom is dented you can also fix that with a repair tool. Your band director might have one, or your local repair shop definitely will. If your mouthpiece is tarnished/dark, you can make it all sparkly and new with this trick.

Personally, I don't replace my mouthpieces when the plating starts to wear through, but you can get them replated or replaced at that point.

If you want to blow $50-100 on trumpet stuff, buy some sheet music or a new mute 😁

Grab a bottle of Al Cass valve oil, a bottle of a bit thicker oil, like Hetman #12 or #13, then some Bach pink tuning slide grease. The Al Cass will be used on the inside of the valves and the Hetman will be used behind the valves and under the valve cap. These three should last you a very long time. I've had my bottle of Al Cass for 3 years now, and my Bach grease for over 5. You'll eventually also want a mouthpiece brush and a lead pipe snake.

In terms of books, it depends on how you learn. If you know nothing about reading music, you can pick up one of the beginning band method books like Essential Elements, but if you are easily bored by simple melodies then this book might not be the one for you. If you are a reader, you may want to consider picking up a horn pedagogy book like Farkas's The Art of Horn Playing, Frøydis Ree Wekre's Thoughts on Playing The Horn Well, or Eli Epstein's Horn Playing From the Inside Out. These books are geared more towards someone who already has some facility on the instrument, but if you lack a teacher, they contain information on things such as embouchure formation, breathing, articulation, dynamics, range, and other things.

The most common etude books are Kopprasch 60 Selected Studies and Maxime Alphonse Deux Cents Etudes Nouvelles, but even at the beginning they are pretty advanced with regard to range and technique. I'd start with Getchell's First Practical Book of Studies for French Horn. There is a second book to this series, but at the end of book one you may want to jump to Miersch's Melodious Studies for French Horn. At the end of that book, you can probably make the jump to Kopprasch.

I'd also grab a scale book like Pares Scales for French Horn, though at the beginning it may exceed your range, so it's fine to wait on this one.

If you have any other questions, let me know!

Edit: as /u/Conn10D said above, I'd highly recommend getting a teacher. Even a month of lessons is enough to nip problems in the bud before they become bad habits that hinder your progress and ultimately take the fun out of it.