League of Legends XXXIX: Harrowing in the Playground

[Nix Nihila]

Quick question (I'm a bit new to League, so please forgive any silliness). How should one go about building Anivia? Particularly her first few items. Tear into Rod of Ages seems to be reasonably popular, but I've also seen a few pro players (such as scarra, and I think RapidStar) start Chalice -> Catalyst -> Athene's -> Sorc's -> Banshee's. Obviously this would be good against a heavy magic damage team, but is starting with a quick Athene's still alright versus primarily AD teams? Would you grab a RoA next in this case?

Anyways, those are my specific questions, but any thoughts on building Anivia would be very helpful.