First and foremost, willingness to learn and a good attitude!
 

Practice time OUTSIDE of lessons and/or band rehearsal.

Ideally, 15-30 minutes per day for beginners, 20-45 minutes per day for intermediates, and 45+ minutes per day for advanced students.

I understand that it can be tough to find time to practice every day, but the commitment to SOME practice every day is the most important thing, even if it's not quite up to the levels above.

I also understand that is a fairly large time commitment.  However, music lessons are not cheap and my assumption is that if you are willing to pay for lessons, you should be willing to practice so that you get the most out of those lessons.
 

A notebook where I can write down weekly practice plans and practice logs.

This can be a traditional notebook or music staff paper.
 

Material that you want or need to learn.  Don't show up to the first lesson with just your horn or we'll be doing long tones and lip slurs the entire time.

(Note: lessons may be only long tones and lip slurs even if you do bring practice material.)
 

For beginners (less than 2 years), I like to use the My First Arban book, which can be purchased here.  (Trombone/euphonium link)

This a great book specifically for brass instruments that will supplement band material.
 

For more advanced students, the variety is greater, but here are a few books that should be in the repertoire of any serious brass student, listed in very rough order of importance:

Arban's Complete Conservatory Method for Trumpet - Called by many the "Bible" of trumpet/brass playing.
Clarke Technical Studies for the Cornet
Schlossberg Daily Drills and Technical Studies for the Trumpet
Concone Lyrical Studies for the Trumpet or Horn
Bai Lin Lip Flexibilities for All Brass Instruments
Charlier: 36 Etudes Transcendantes for Trumpet
Vizutti Trumpet Method Book, Technical Studies

There are many, many more great books out there, but these are a solid foundation for all brass-related technique development.

 

Warmup and basic technical exercises PDF.  This is my preferred warmup and a collection of my favorite technical exercises.  Everyone's requirements are unique, but this is a great jumping off point for developing your own warmup routine.

Generally speaking, your warmup should take 5-15 minutes and should hit three main areas of embouchure development: long tones, lip slurs or lip flexibilities, and tonguing.  These three areas are the foundation of building a healthy brass embouchure.