I am a high elo LoL player trying to help out some of the new players decide what items to build since there are a lot of items in the store. Items should be built depending on the flow of the game and based on the enemy team but I have put together a list of the best items that work in all situations. Theres a few ways to build Annie, the rod of ages route or the dorans deathcap route. I'll show you both.

You can interchange the Q and W at level 1 but the W is helpful because you can charge up your stun in base with your W. Skill order priority R > Q > W > E

You can interchange between Rylais, Zhonyas, Abyssal Scepter, and Deathfire Grasp or some defensive items such as Banshee's Veil and even Guardian Angel depending on the situation. All are viable options at all elo.

Flash and ignite are definitely recommended. Flash keeps you safe and it also allows for some great ganks with your jungler. You can build up your stun and flash stun the enemy while your jungler comes to gank for a pretty much guaranteed kill with Annie's insane burst.

You want to be involved with your team early game on Annie due to her incredible burst at level 6. You can roam and gank after pushing the lane to help pick up some early kills and help you push your advantage into late game.

Annie's farming is really easy due to her aoe damage and the fact that you have endless mana when farming with her Q. Each time you last hit with her Q, the mana cost is refunded. Also, her auto attack range is very far so it allows for some safe farming and some easy harass during lane.