On the subject of which excerpts from that book to select week to week, I would encourage *not* going through the book in page order, but rather picking from each of the major sections (as Dave mentioned, the book is sorted by Marches, Transcriptions, Original Band Compositions, and Orchestral Transcriptions). This way by the end of your school term/year, you have a good understanding of the various excerpts and major styles.
For audition lists, usually you can find old lists in pdf format by doing a general internet search and looking around the various military branch band websites. This search will help inform you of what excerpts tend to appear on audition rep lists. Stars and Stripes is definitely one that shows up fairly often, same with at least one of the Holst Suites, and something by Grainger (such as Colonial Song, Lincolnshire Posy and Molly on the Shore).
Side note: 1-2 march excerpts are essentially guaranteed to show up on any military audition rep list, with usually one by Sousa, so you'll definitely want to be familiar with the march style and unwritten performance rules that accompany them. There's a fantastic video by two euphonium players in The President's Own that provides an overview of march style. Highly recommend checking it out!
Here's a link to that video: https://www.youtube.com/watch?v=f9kibOSP7sU
Willson 2900 TA-1 Euphonium - Denis Wick 4AM
Yamaha YSL-643 Trombone - Bob Reeves BrassArk 5G "Gladstone"
Yamaha YSL-8440 Trombone - Denis Wick 5BS
VMI 3301S BBb Tuba - Schilke Helleberg
Past:
York Preference 3067 Euphonium - Denis Wick 4AL
Benge 165F Trombone - Benge Marcellus
Wessex BR140 Baritone - Denis Wick 6BS
F.E. Olds Special Trombone (ca. 1941)