Finding or reviewing repertoire are technical procedures to be accomplished as quickly as possible, so that you can get to the real issues: solving vocal-technical issues, analyzing the lyric and dramatic purpose of the song, and making the song "yours" i.e. not merely a piece of material you perform, but crafting a completely integrated, unique, and unassailable performance.
Vocal coaching versus voice-teaching: early on, I made it my business to study voice, specifically to enhance my coaching of others. I studied first with Carmine Gagliardi, who was Patti LuPone's teacher and Hal Prince's vocal-technique guru of choice in the late '70's and early '80's. For many years now, I've studied with voice teacher and vocal therapist Dr. David Fairchild, who has taught Donna Theodore (Tony nominee and Theatre World Award winner for Shenandoah), Rikki Lake, Kate Hunter Brown (The King And I with Yul Brynner), Chloe Webb, Gerard Alessandrini, Leila Martin (Phantom Of The Opera), Toni DiBuono (Forbidden Broadway), and Regina O'Malley (On Your Toes, Les Miserables).
I offer vocal technique for those who want or need it, since vocal issues can be the first disqualifier in auditions; even the most accomplished singers can find it handy for unique challenges in certain material. Actors-who-sing can land great roles very handily with even a few simple vocal tips.
The other main vulnerability I have observed in thousands of auditions over the years is the acting, whether in the song or the scene. Many terrific singers in both the musical theatre and cabaret worlds haven't prioritized acting in their training, and current standards of musical theatre acting are uneven from genre to genre. Acting should drive the musical performance not the other way around. When I music-direct, I conduct according to the performer's acting performance and in a coaching session, I have various methods to help the performer live and breathe the material in real time.
Repertoire: one look through your book will inspire a list of what I think you need, if anything (if you don't have a book of at least ten songs, I'll fix you up with one immediately).
As a bonus, I'll help you prepare sides, or a role; I have a director's eagle-eye, which many clients have found helpful, particularly for cold readings.
Contact me about my hourly rates. My version of an hour is frequently more than sixty minutes, if we get on a roll.
P.S. A word about auditions: I'll run downtown and play your audition, and this is frequently advisable. It's not always necessary but I'm there if you need me.