Ignite and Flash are both very strong for Annie as soon as you can get them. I personally like Neigan's build, which goes Boots of Speed -> Haunting Guise -> Ionian Boots/Merc Treads/Sorc's -> Catalyst -> RoA OR Banshee's (the latter if opponent is caster based) -> Rabandon + Zhongya's -> Swap Guise for Void Staff if you need more Magic Pen.
Of course, this isn't the only build, and some may think it sucks. However, I find it very effective.
If you don't know already, Annie is the queen of the early - mid game. She CANNOT hard carry her team to the end game, so you have to do the best you can before the end game and try to feed your carries. Try to get Solo Mid, even if it means having your carry do Solo Top. Annie requires the exp advantage to nuke - otherwise, all she has is her stun. Harass while last hitting with your Q. Don't be afraid to waste your stun, as without Tibbers your stun won't help you much. Once you hit level 6, you can start saving up that stun, even if it means spamming W before a teamfight. You should definitely invest in wards, especially after first blood/a kill, and gank! Annie snowballs very well (especially with Mejai if you know that you can get a lot of kills). Feed your carries, and try to push as much as possible after a gank/teamfight in your favor. Buy wards as much as possible if you get a lot of kills.
In the late game, your main asset is your stun, somewhat nuking potential (or huge nuking potentiail if you're REALLY fed ), and warding out of the gold you should hopefully be getting from kills.