My personal suggestion:
1. Eyes
2. Hair
3. The tsundere "angry at you" pout.
#1. It's not an anime without the anime eyes, plus, more than half of the facial expression battle lies in the eyes... Wide open eyes, half-open eyes, squinting eyes—is the iris small (scared/shocked facial expression), is the iris looking up, looking at a nearby object, looking into the far distance, what is the difference between the closed eyes U-shaped (UwU) vs "upside-down U" shaped?
#2 is self-explanatory. Get the eyes and hair right, and you've practically got the anime right. There's three parts to the hair: bangs, side, back. For me, the bangs and back are what matters. Find an artstyle you like and copy its bangs. Learn to draw ponytail, sidetail, birdtail, with hairband, etc. Everyone has their own way of doing hair, so make sure you only copy hairstyles you like.
3. I can't post a link yet because I don't have enough community points. But what I consider my personal "renaissance" when it comes to the anime artstyle, is being able to draw the "tsundere face". Face slightly tiled downwards, eyelids closed halfway, eyebrows knotted in V-shape. For something close, look at 5-Toubun no Hanayome's manga pouts. Look at the halfway-closed angry eyes.
Get the tsundere right, and you can show all your friends how anime you are.