Melinda values several elements throughout Anderson's novel.  It is needed to distinguish Melinda's life as pre- attack and life after it.  I will focus on the latter.  I think that one of Melinda's values that she learns is the power of voice and the ability to "speak."  It might seem rather weak to suggest that this is a value, but it is a valid one.  Melinda remains silent throughout the work until the end when she confronts "it" with her defiant voice of "I said 'No!"  In this light, the power of voice is something that Melinda values greatly.  At the same time, Melinda values the power of transformation and change.  There are points of this in the work.  When Melinda wishes to "go back" and "replant herself" as a seed in the ground, it is testament to how much she has come to value the power of change.  Melinda is a person that has grown, similar to the tree from the person who she was into the person she could and should be.  The power of change is something that Melinda values.  Finally, I would say that independence is something that Melinda values.  I think that the last thing that Melinda values is redemption.  Melinda values redemption in that she does not stay huddled in her silence, passively receiving life.  Slowly, she emerges.  Writing in the bathroom wall about Andy, seeking to bring others into her own experience like Rachel, and even opening up to the art teacher at the end are all instances and examples of how Melinda represents a sense of redemption and the belief that individuals can experience a sense of happiness at the end of their struggles.  Melinda believes in those values of self improvement and the striving for perfection that allows individuals to become better, to move from bad to good and from good to great.

What does Melinda want in Speak by Laurie Halse Anderson?

This is a hard question. Melinda wants all kinds of things, and she wants them at different times for different reasons. At times, Melinda wants to be left completely alone. It's why she hides in the janitor's closet so much. She's afraid of certain people in the school, and she doesn't enjoy being treated like a pariah. Being able to completely withdraw is tempting for her.  

Probably more than anything, though, Melinda wants to be able to talk about what happened to her at the party. She wants to tell people about why she called the police. She wants to tell people the truth about Andy. Melinda can't, though. She is too scared and ashamed of being raped. She doesn't know how to tell people, and a major part of the novel is about Melinda growing emotionally and psychologically strong enough to speak out.