1. Horizontal wove paper showing strong ribbing on both the front and back of the stamps.
2. Horizontal ribbed paper showing ribbing on the front only.
3. Horizontal ribbed paper showing ribbing only on the back.
4. Horizontal wove paper showing no ribbing at all either on the front, or the back - the horizontal mesh only being visible when the stamps are held up to a strong light source.
5. Vertical wove paper showing no visible ribbing.
6. Vertical wove paper showing distinct vertical ribbing on front and back.
It was suggested in one philatelic article (I can't remember where) that the vertical and horizontal papers were the same and only reflect the fact that the printing plates were rotated in late 1958 from a horizontal orientation to a vertical one. However, close examination reveals that this is not the case. The appearance of the ribbing and the appearance of the mesh is completely different with these papers. Also most of the horizontal wove papers are between 0.0035-0.004" thick, whereas the vertical wove papers are usually exactly 0.0035".
Whether all six textures should be represented in a collection is a matter of personal preference. I can see how some collectors may feel that papers 1-3 and 5-6 are the same and that distinguishing between them is overkill. However, I believe that based on their characteristics, at a minimum a collection should feature three of these types.
The scans below show the three basic types: