For all of my builds, my anti-mage strategy has always been incredibly simple: Sneak + Dagger and/or bow (+ Aura Whisper for detection once available). Bows aren't really effective when used in open combat until you can level it up considerably, however combined with Sneak the stealth damage bonus makes it incredibly deadly even at the early levels. When I suspect a mage, I sneak, then either slash them across their throats or headshot them
I've managed all three playthroughs in ever increasing difficulty without once using any magic/elemental resist items/potions.