You already said shoes, but I would add that the shoes need to be appropriate for the type of terrain you'll be running. I live in PA, and our trails tend to be very rocky, so the stiffer the sole, the better.
The other thing I would recommend is a running pack that will hold your essentials, including a water bottle. I found one a few years ago that fits snugly around my waist, so it doesn't jump around while I'm running. It holds my car keys, iPhone, ID, and a water bottle.
