My list of recommended trumpet studies, solos, duets, and recordings:
Author/Composer, Title, Publisher

Studies:

1. Jean Baptiste Arban "Complete Conservatory Method" Carl Fischer
2. H. Voxman "Selected Studies" Rubank Inc.
3. Vassily Brandt "34 Studies for Trumpet" International Music Company
4. Theo Charlier "Trente-Six Études Transcendantes" Alphonse Leduc
5. Herbert L. Clarke "Technical Studies" Carl Fischer
6. Sigmund Hering "Thirty-Two Etudes" Carl Fischer
7. Sigmund Hering "Etudes in all the Major and Minor Keys" Carl Fischer
8. Getchell "First Book of Practical Studies" Hovey
9. Getchell "Second Book of Practical Studies" Hovey
10. Colin "Advanced Lip Flexibilities" C. Colin
11. Goldman "Practical Studies" C. Fischer
12. Stamp "Warm-ups plus Studies" Editions Bim

Trumpet Solos with or without Piano:

1. Leroy Anderson "A Trumpeter's Lullaby" Mills Music, Inc.
2. J. E. Barat "Andante et Scherzo" Southern Music Company
3. Eugene Bozza "Rustiques"
4. Bruce Broughton "Oliver's Birthday" Black Squirrel Music
5. Herbert L. Clarke "Maid of the Mist" Warner Bros.
6. Handel/Fitzgerald "Aria con Variazioni" Belwin-Mills/Warner Bros.
7. Franz Joseph Haydn "Concerto for Trumpet" Carl Fischer
8. Sigmund Hering "Classic Pieces for the Advancing Trumpeter" Carl Fischer
9. Johann Nepomuk Hummel "Trumpet Concerto" Belwin Mills
10. William P. "Latham Suite" John Church Co./Theo Presser Co.
11. Joseph Turrin "Three Episodes" Joseph Turrin Music
12. Antonio Vivaldi "Concerto for Two Trumpets"
13. Kent Kennan "Sonata for Trumpet and Piano"
14. Arban "The Carnival of Venice"
15. Donald Hunsberger "Believe Me If All Those Endearing Young Charms"
16. Maurice Ravel "Piece en Forme De Habenera"
17. Aaron Copland "Quiet City"
18. Charpentier "Prelude to Te Deum"
19. Paul Hindemith "Sonata for Trumpet and Piano"
20. Fischer Tull "8 Profiles for Solo Trumpet"
21. Gordon Young "Contemporary Suite" Belwin-Mills/Warner Bros.

Trumpet Duets:

1. Arthur Amsden "Amsden's Celebrated Practice Duets" C. L. Barnhouse Inc.
2. Sigmund Hering "Miniature Classics" Carl Fischer
3. Sigmund Hering "More Miniature Classics" Carl Fischer
4. Sigmund Hering "Trumpets for 2" Carl Fischer
5. Sigmund Hering "Bach for Two Trumpets" Carl Fischer
6. H. Voxman "Selected Duets, Volume I" Rubank, Inc.
7. H. Voxman "Selected Duets, Volume II" Rubank, Inc.