Try starting with "squaw wood." This is deadwood and twigs still on the tree (off the ground) and in arms reach (don't have to bend over to pick it up). Generally, this wood will be fairly dry shortly after a rain.
You could locate some "lighter" or "fat" pine. That is pine that is full of sap. Remember that pine sap is the basis for turpentine. "Fat" wood smells like turpentine and looks sort of wet. It lights real easy. It is hard to clean up after so use it only for starting the fire, not for cooking.
It is critical to start small and build slowly when using damp wood.