Rain gear is the only thing you really need. DriDucks are good. Bring duct or Tyvek tape for patches.

I have trekking poles, but I've stopped bringing them.

You could cook over a small twig fire, or go cookless. I usually use a fire.

A filter or chlorine dioxide tablets might be a good idea. I often drink water straight in wilderness areas, but with careful consideration of the water and the risks.