Also identifying a professor with whom you would like to work towards your PhD is also important. After identifying you should establish contact with the person and tell him that you would like to work with him. If the prof finds that your research interest matches with his, then he might get tempted to take you. About Ivy League, I had a not so pretty experience two years back- I had written to two Profs. of an Ivy Institute, they didn't reply back. I just gave up on them and their institution. Talking about GRE, I had one senior in school, she had less than 1400 in GRE, yet she went to an Ivy school for Doctoral Studies - she got fully funded for five years. She had enormous experience in theatre, had already directed a couple of plays.