Don't give the pianist hand written sheet music. Unless your handwriting is impeccable, if the lighting is bad or the chicken scratch on the page is too small or indiscernible, your pianist may have trouble reading it. My friend Mike is an excellent pianist but he is too proud to admit that his vision is beginning to fail. He is not going to be wearing glasses so both you and he are automatically at a disadvantage. Don't let his pride make you sound terrible. Give him something easy and clear to read.
Don't provide music written in keys with too many sharps or flats. Even if you are auditioning for a professional theater company, maybe they're regular pianist couldn't make it and the union sent over some new person without a lot of sight reading experience. Again, don't make it difficult for the pianist to make you sound good. Have the music transposed up or down a half step where it may be easier to read. You can either purchase music in various keys online or input it yourself into a program such as FINALE or some other engraving software. Many simple engraving programs can be found for free online.
Don't hand the pianist a brand new book with an uncooperative binding. New books which don't already have the binding broken can close on its own at any time. Wouldn't you rather the pianist to be focusing on you and not holding the book open?
If you are going to tell the pianist that you want to "Start here," then "skip to here," "repeat to here," "skip this page," "I'm singing different words here," "I'll stop there." then clearly mark it out in advance and use colored highlighters. Better yet, have the music re-transcribed using a program such as FINALE and lay it out exactly as you wish to sing it so that the pianist doesn't have to navigate a maze of clues, scribbles or even trust their own memory.
Treat your pianist with respect, even after you finish singing and are walking off stage. I once worked at the Empire State Institute for the Performing Arts at The Egg. Our music director was named George. He was a wonderful man who always watched the interaction between the singer and pianist. There were times when George would come down to the pit and ask me what someone said to me or what the music looked like, did they say "Thank you" or if I thought they knew what they were doing. How they treated me, how prepared they were and how easy they made it for me, mattered to George when hiring future cast members.
When it comes to having your music in a key you want it in, use a music engraving program and have your music transposed in the key you prefer because not every pianist can sight transpose. Even though I can sight transpose very well because it is something I do every day, it would behoove you not to test me at YOUR audition. I used to work at the Emma Willard School playing for four ballet classes a day, seven days a week and the teacher would only allow me a repertoire of 50 specific songs. Her reasoning was that she wanted her students to know the music so well that they would be better dancers. I quickly memorized the music and on some days, in an effort to entertain myself, I would transpose everything up a third for instance, or play everything in the key of B, then Db tomorrow. So, it's your audition. Do you want to risk sounding bad because you took a risk on the pianist?
Some pianist can fake an accompaniment with just a lead sheet and chords. If your pianist can't read chord symbols and you present them with only a melody line, you're sunk.
Some pianists can't read bass clef very well so if your music also contains chord symbols at the top, that can be very helpful. Even if I am reading both clefs, sometimes having a chord above the melody line can aid me in difficult passages. Many pianist will utilize both tools in accompanying. Have a friend with a knowledge of music theory neatly write the chords in if they are not already there.
Some singers may bring in their own pianists. My friend George wouldn't have allowed that because he wanted to see how you worked with new people. It wouldn't hurt to call in advance to find out if they will allow you to bring your own accompanist. Many won't mind.
Some singers practice with a recording and are comfortable singing to that karaoke type recording. Again, directors may want to hear you with only a piano or their pianist in an effort to discern your flexibility.
Some singers ask if they can sing a Capella. Many music directors will want to hear you with a piano to see how quickly and efficiently you can match pitches and rhythms. Some directors will allow you to sing unaccompanied but won't consider you. You will be giving them a much needed two minute break.
You may be able to wow the directors with your rendition of a Sondheim piece or some other difficult work, but your pianist may not be able to. It is you who may suffer when a pianist struggles with a difficult score. The pianist already has the job. Consider keeping it simple.
If you absolutely must sing Sondheim or something from a difficult score, pay someone to simplify the arrangement so that it is easy to read and play by the average pianist. Give it to a pianist friend and see how well they can play it on sight.
A few directors may frown upon you if you bring in illegally photocopied sheet music, just a few. Personally, this is the format I prefer. If you give me single sided, numbered, loose pages, I can lay them out on my music rack or stand with little fuss. Just keep it down to three or four pages. If one accidentally goes flying, you're up the creek. I don't mind if they are in a binder either but, they should then be double sided. Don't put them in a binder with hundreds of other songs and the whole collection weighs a lot. If I am using a music stand, it could cause my stand to slide down. Don't put your music in those plastic sheet protectors, either. Depending on the lighting they can cause a glare making it difficult to see the notes.
It never mattered to me if the singer sang a song from the show they were auditioning for or, sang a song that the character they were auditioning for will sing. However, if you are asked to hang out for a call back, you will probably be asked to sing something from the score. I once played an audition for CAMELOT in NYC. We were only casting for the two parts of Guenevere and Lancelot and over 300 people showed up. It was amazing how many men didn't know the song "If Ever I Would Leave You." It really showed us who would require a lot of hand holding and note plunking if they were cast in the show, which they weren't.
No matter how good the pianist may be, let me reiterate, don't make it difficult for them to make you sound good. If you are good, your quality will shine through on anything you sing. No matter how badly a piano player may butcher your piece, the director isn't listening to the pianist but they may take notice of your composure and recovery skills or, lack thereof. Keep it simple.