Wands and spells (e.g. Harry Potter)
Magic is instant but you need a staff, wand or something to cast.
Body movement magic (e.g. Avatar, Korra)
Magic is instant, requires martial-arts like movements to cast.
Tutting (e.g. The Magicians, Dr Strange)
Magic is instant, requires complex finger movements to cast.
Symbols and Circles (e.g. Dr Strange, FairyTail, Fullmetal Alchemist)
Magic is instant, requires complex patterns (like a transmutation circle) to cast.
Ritual magic (e.g. AHS: Coven)
Requires long rituals and usually have non-instant effects.
Let me know if I’m missing any and let me know which you’re using!