Right now I only have the Arban, but I’ve been wanting to buy more books to read from for some time now, and, ultimately, have a mini library. Any suggestions for fun or helpful books?

Rochut's Melodious Etudes. <LINK_TEXT text="https://www.carlfischer.com/o1594x-melo ... 60-29.html">https://www.carlfischer.com/o1594x-melodious-etudes-for-trombone-28book-1-3a-nos-1-60-29.html</LINK_TEXT>

Go on IMSLP and get the following (for free)

Simone Mantia "The Trombone Virtuoso"

Blazhevich, "School for Trombone" (we used to call this "Clef Studies")

Jaroslav Cimera, "55 Phrasing Studies" (This is like a preparatory set for Rochut)

I also have a scan of a method book by Carl Hampe that contains some very easy and some very difficult exercises (contact me privately).

Some other methods to get for your library:

Rochut, "Melodious Etudes" (in three volumes. Get Volume 1)

Remington Warmup Exercises (Get the version edited by Hunsberger)

Pasquale Bona, "Rhythmical Articulations"

I'm sure others will chime in.