Method Books I Recommend in no particular order:
Arban Complete Method - Joseph Alessi and Brian Bowman Edition
Rubank Beginner/Intermediate Methods
Max Schlossberg - Daily Drills and Technical Studies
Bordogni/Rochut - Melodious Etudes
James Stamp - Warmups and Studies
Charlie Vernon - Daily Routines
Vandercook - Trombone Gems
Remmington - Warm Up Studies
Marsteller - Basic Routines
Everything Arnold Jacobs ever said
Advanced:
Sam Burtis - The American Trombone
David Baker - Contemporary Techniques for the Trombone
Stuart Dempster - the Modern Trombone
Jen Baker - Hooked on Multiphonics
Edward Kleinhammer - The Art of Trombone Playing
Yusef Lateef - Repository of Scales and Melodic Patterns
Slonimsky - Thesaurus of Scales and Melodic Patterns
Apps for Practicing:
Tonal Energy Tuner
Drum Genius
iReal Pro
ForScore
Some Trombonists to listen to (in no particular order):
Christian Lindberg
Joseph Alessi
JJ Johnson
Bob Brookmeyer
David Taylor
Melba Liston
Jimmy Knepper
Urbie Green
Mike Svoboda
Alain Trudel
Ralph Sauer
Luis Bonilla
Jorgen Van Rijen
Lawrence Brown
Abbie Conant
Al Grey
Jack Teagarden
Branimir Slokar
Ed Neumeister
Rita Payes Roma
Willie Colon
M. Dee Stewart
Denson Paul Pollard
David Whitwell
James Markey
Granchan Moncur III
Charlie Vernon
Peter Ellefson
Juan Tizol
Ray Anderson
Julian Priester
Bill Reichenbach
Albert Mangelsdorf
Roswell Rudd
Brian Hecht
William Lang
Jen Baker
Jacob Garchik
Steve Swell
Frank Rosolino
Marshall Gilkes
Tommy Dorsey
Glen Miller
George Roberts
Nils Landgren
Kai Winding
David Baker
Stuart Dempster
Curtis Fuller
Kalia Vandever
Bill Watrous
Fred Wesley
Colin Babcock :)