If you are applying to several different schools using one generic statement will be easily recognized and just as easily dismissed. WHY _ because you will be seen as not making an effort sell yourself to this particular school, low effort equals low interest to admissions representatives. Remember the admission committee will likely view thousands of these statements from qualified candidates and they will spot a weakness, flaw or lack of attention to the process in a heartbeat. What you don't want to do is give this committee an easy excuse to dismiss your statement and application.
One approach is to begin with an interesting statement, then follow it with a brief overview of your main theme. e creative with your introductory paragraph. Another approach to make it unique is to use personal information that distinguishes you from the rest and makes the essay stand out from others. Another approach is to use a fact or a literary concept, which is relevant to your theme. Paraphrase it or use a direct quote, and add in whatever point you are trying to make. As much as you would like to present a good introduction, do not fall into the trap of making hasty generalizations, sweeping statements, and/or other pronunciations. Keep the tone light and personal. After all, you are telling your own story.