Tick anything you already have, in any order. Quests unlock once this is done.
Ivory-type bars carve best because they are soft and have no grain. This is the cheapest way into carving anything, which is exactly why it is worth doing first.
One thing left above. Quests are real things you go and do, so they only make sense once you have what you need.
First one waiting: Carve a bar into a smooth simple shape