Rylais if your team lacks gap closers to secure kills and escape to disengage bad fights.

Protobelt if you need some more mobility because enemy has gap closers or heavy on slows.

Ludens if you are not behind and can afford it. But I would opt for Rabadon if you're that far ahead. It's certainly not a rush item for Annie.

I usually do: boots -> 1 core offensive AP -> 1 core defensive AP -> void staff -> items for specifics of the enemy comp and game situation

If we have no frontline, my core offensive will also include HP, and my core defensive will include a resistance for whichever enemy is furthest snowballed. If none, then build the resistance around their average AD/AP ratio.