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for beginners: Walter Beeler Method for Euphonium. (or Beeler Method for Trombone).

The Beeler book is better than the Rubank Method for beginners. Rubank goes too high, too quickly (D above the staff within the first 10 pages).

advanced beginner to intermediate: Hering's "40 Progressive Etudes" (trombone) is a good book with etudes that are about a page in length. These work well for somebody in their first to second year of playing.

Bordner (Practical Studies?) has short excepts that work well for short attention span students. They tend to be fun to play and build confidence. I use them for decent musicians who are switching to euphonium. These are similar to the Getchell Practical Studies for tuba, but for trombone/ euph.

Caveat, they do not do a lot for developing musicianship. But for learning which fingers to put down it is a solid book. Because 16th notes come early, the book appears harder than it really is. Most student would hate practicing if they had to go back to "Hot Cross Buns."

C'mon. Go for the Arban's trombone.

I use the Beeler for baritone with all my beginners. It is helpful because it gives fingerings to new notes as you encounter them. It also gives you reminders to fingerings as the mix gets more advanced. You may also consider using "5 Minute Theory" by Mark Wessels as a work book supplement.
http://www.mwpublications.com/Merchant2 ... e_Code=MWP