Tick anything you already have, in any order. Quests unlock once this is done.
A faceting machine is several hundred at minimum and clubs have them, along with people who will teach you the angles. This is how nearly everyone starts.
Find a lapidary club2 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: Start at a lapidary club or workshop