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Build Guide by Cheebamaster
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Abyssal scepter (if you're against a heavy AP team)
Banshees (6th item vs ap nuke team)
Hourglass (situational but good to get if you're constantly being focused
Rylai's is a flavor item. The extra hp is really not needed but if you find you're being focused it's not a bad choice for a 6th item.
If you find yourself in a troublesome situation and you know that running will only get you killed, you may as well stay and fight. Annie does a very suprising amount of burst damage and I can count more than one occasion in which I killed someone just by staying in fighting rather than running.
I highly suggest getting a Mejai's on Annie once you are comfortable. My general sequence is to rush catalyst followed by boots and then rush mejais.