Write in the first person, but don't overuse "I." It shouldn't be a research paper, no. But it needs to be PERSONAL (hence, why it's called a "personal" statement). Hence, a good blend of personal, but not too casual, writing along with a certain level of formality is good.
Feel free to e-mail me for more advice. I've been through this process, and my personal statement got me into Harvard, so I know quite a bit about it.