Tick anything you already have, in any order. Quests unlock once this is done.
A frame loom is under twenty and teaches the same over-under. A floor loom is a piece of furniture and a serious commitment, so it is not where anyone should start.
2 things left above. Quests are real things you go and do, so they only make sense once you have what you need.
First one waiting: Get a small frame or rigid-heddle loom