Wood comes from salvaging a variety of weapons. Staves and Bows will grant the most but you can get some from maces, swords, axes, etc. Shields also.
The tier of material you get is determined by the weapon tier, if you need Plain Planks to upgrade the forest to Rank 2 you will get them from "Plain" and "Iron" weapons of the types mentioned above. These items will drop from any level 15-49 monsters.