Be honest with yourself when determining your vocal style. If you are a baritone, don't try to make yourself into a tenor simply because you long to play a tenor role. Sticking within the limits of your natural vocal range will assure you a much more solid performance than if you were to reach outside your realm of natural capability. Simply be yourself! The musical-theatre genre has expanded to include many different vocal styles. It is no longer necessary to have an operatically trained voice to land a part in a musical. In fact, many modern musicals lead much more toward a rock tone, requiring a more raspy, passionate voice. To accurately determine your vocal style and range, you may consider undergoing a one-time vocal evaluation. A vocal instructor can easily determine your voice-range classification, and can perhaps even make some valuable song suggestions.
Choose a song you like. Pick one that complements not only your voice, but your age and personal style as well. Do not chose a song from a role that you could never qualify to play; if you do, the directors will simply be confused by your choice, instead of paying attention to your voice. Choose a song you're passionate about. Listen to as many clips of musical-theatre pieces as you can find online. Hold out for one that matches your vocal talent, as well as affects you emotionally.
Never choose a song from the musical you are auditioning for, unless the audition guidelines specifically request that you do so. Directors have very specific ideas of how their productions will turn out, and singing a song from their current show in a manner that doesn't fit their vision is a sure way of losing out on an opportunity. Instead, choose a song from a musical with a similar style, or one by the same composer. This will allow the directors to easily imagine you in the role, while not offending any of their specific intentions.
Once you have selected your song, obtain the sheet music and/or an accompaniment CD. It is always a good idea to have both, so your options for music are not limited at the audition. Practice both with the CD and with a trained pianist.