The most durable carpet is nylon and it's the most common carpet material too. It's the strongest fiber, making it an excellent choice for heavy-traffic areas.
Buy Rapier from the Undead Merchant. Anything should be effective at this point against the Taurus Demon though if you utilize the Gold Pine Resin before the tower you climb...
You can get them from Daedric quests such as Umbra, in which you could get from the Clavicous Vile quest. But you could find them from normal quests such as...
Smite V on a diamond sword (22.5 damage vs. 13 damage with Sharpness V). Don't use Knockback, because it will be annoying; every time you hit the Wither he'll be...
Shade cloth can withstand about 14 pounds of pressure, but be aware, this material is often used for covering objects. Check the brand of the cloth to make sure.