I have two standard tips for picking the perfect audition song/s first time, every time. I'll lay them out first, and then I'll explain why.
My Two Standard Tips for Picking the Perfect Audition Song/s First Time, Every Time*
(*because is there any another option?)
Tip 1: Songs in the style of the show are often in the style of the composer, so why not start with some of their other works? Nothing shows you can sing <insert composer name here> like singing <insert composer name here>!
Tip 2: Think about the character you're auditioning for - what are their wants? Their troubles? Their dreams? Once you've worked that out, try and find a song from another show that relates to your character's situation somehow. E.g., if you were auditioning for Eponine in Les Mis you could try "I'm Not That Girl" from Wicked - see the connection? That shows me, as a member of the audition panel, that you've put some time and effort into your song selection, and thought about the character (remember what JRB said?), rather than someone who always sings the same two songs, no matter what show they're auditioning for.
Now, before I get to the 'why', I have a question: what happens in the callback that you don't get to do in the audition? Any ideas?
You get to sing one of the actual songs sung by the character you're auditioning for
That's exactly what you DON'T get to do in the initial audition, but remember - audition panels are lazy. They don't want a project they can work on for a few months, they want a performer they can slip into a costume and slap on the stage.
So, why my two tips?
They give you the opportunity to let the audition panel see you perform in
the context of the character that you wouldn't normally be able to do until the callback
That's it. Rather than singing two completely random songs, that, sure, may be great for your personality/voice, help the panel 'see' you in the role as quickly as possible by tailoring your songs to fit that role. It sounds ridiculous to actually have to say it, but we see people making this mistake all the time. My favourite story involves an auditionee singing a reggae version of "Under the Sea", accompanying themselves on the guitar, in an audition for Into the Woods. It probably comes as no surprise that they didn't get in.
But what if I'm not auditioning for a role, I hear you ask?
Well I say, why not? Doesn't hurt to aim high. Better to aim for the lead and get it or end up with a supporting role than not try at all. I recently had a student cast in a (hard and lead) role he didn't even audition for and he worked his butt off for three months and totally nailed it. You'll never know unless you try, and all that.
Yeah but the person who wrote this show hasn't written any others, so your first tip is flawed
OK I must admit this is sometimes the case. So then it's time to get creative. If you can't use something from one of the composer's other works, aim for Tip 2 - find a song that suits the character's situation, then contrast it with one that shows off your voice. Or if you don't like anything from the composer's other shows, some writers, such as Jason Robert Brown and Duncan Sheik, have written solo albums that, although technically not musical theatre, still reflect their own particular style. If you look even further, Bobby Lopez (Frozen, Avenue Q) wrote the music for the Scrubs musical episode and ps classics released an amazing posthumous album of Jonathan Larson's original demos and other material^ (Wikipedia can be your friend with this stuff). There's always something out there if you look hard enough. And one final bonus tip is to look at other material the performer of the original song has sung. Much like finding your 'box', most of Idina/Sutton's songs have a similar sound/style so that may be another good starting point when thinking about songs that suit your character. :)
What about developing an audition/repertoire book?
I guess it doesn't hurt, but I can pretty much guarantee, no matter how many songs you end up including, it will never have the exact perfect pair you need for that particular show. Sure, it's possible, but I highly doubt it. Better to prepare individually for each and every role, tailoring your songs to the exact character using the tips above. But if you do want to take the audition book path make sure you have something from every era/style: pre-1950s ballad, pre-1950s upbeat, post-1950s ballad and upbeat, comedy number, belt extravaganza, etc. Better to cover all bases and make sure these are songs that you regularly revisit/keep fresh in your mind as it's no use having the book if you can't all on it with as little as 24 hours' notice.
^ Wearing Someone Else's Clothes and Jonathan Sings Larson both feature early songs cut from final versions of the shows - worth a listen purely for interest's sake.