your ideas are good. Although I might say that a neophyte could be shown various basics of different modalities (say making potions). When they show an aptitude for one, their main focus might be there. For example, I have no interest in "high" magic. Simple approaches work best. So I would continue to learn "low" magic like herbalism
There might be psychic tests involved to see about innate gifts (find the egg, only using closed eyes!)
symbolism is important to all aspects of magic, and there's a lot of it. You have rune forms, nature symbols, glyphs and wards....