If there's one thing you never want to happen during an audition, it's for someone else to audition before you with the same piece you're doing. It's a horrible feeling (speaking from experience), and it tends to happen to those who choose very common monologues and songs (think Juliet from Romeo and Juliet, "Defying Gravity" from Wicked, you get the idea). Finding pieces that you feel you would perform well with and that aren't overdone is a HUGE part of this process. 

Start reading plays if you want to find good monologues! Find a local bookstore or library and read through their selection of plays! I discovered some great plays by visiting my local bookstore, one of which I used during my prescreens! I'd also recommend reading the New York Times theatre reviews for plays to see what new plays have received rave reviews.

Also, some schools have specific requirements for the types of pieces that must be performed during prescreens and in-person auditions. Some of the schools I applied to, for example, required two contemporary monologues, others one contemporary and one classical, and others left it entirely up to you. Some schools also required all pieces to be within your "age range," which for students applying to colleges means characters between the ages of 18 and roughly 25, so age does matter when looking for monologues, especially since older characters can be much more difficult to play because you as a young person haven't experienced many of the things they have. So, make sure you check the audition guidelines on each school’s website, this will help inform you as you start finding materials. 

For songs, I'd recommend either spending some time listening to some more underground musicals that may have some songs that people haven't heard before, or asking people what they have in their rep books! It might seem like backward thinking, but it can be extremely beneficial at times. One of the people at SUTE suggested I listen to "A Little Bit In Love" from Wonderful Town, and I used that song for three of my auditions! Looking at what others are singing can definitely help you find songs to check out that might help you later on!