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I find with this setup my annie becomes very difficult to kill throughout the game and I become more effective in team fights because they have a much harder time killing me, while I still maintain alot of the bonuses needed to be an effective annie.
These are all about your playstyle and personally I think people should use whatever they are comfortable with.
I start with a Regrowth Pendant.
You don't need any mana regen early because if your good at last hitting with disintegrate your natural mana regen will keep up with any harassing you do.
Now after that...
Philosophers Stone --> Once you start spamming spells the mana regen does come in handy.
Tear of the Godess --> This will increase your health regeneration as well as your ability power later.
Sorcerers Shoes --> Move speed is crucial by the time this point in the game comes around.
Rylai's Scepter --> Health and your non Pyro'd abilities now slow as well.
-->Depending on how the game is going your next item can be either completing Archangels Staff or getting a Meijei's Soulstealer. I recommend going Meijeis if you think that your going to be getting alot of kills, otherwise skip it and go with Archangels.
Archangels Staff --> At this point you want to start getting your ability power up.
Zhonya's Ring --> This Should jump your ability power up into the 400-500 Range if you've been casting alot of spells and got your tear/archangels nearly maxed out.
From here you have a couple of options... Here are some I recommend.
Abyssal Scepter --> Increase your spell damage as well as lowering their resists (Get this only if several people on your team are doing spell damage and no one has it yet.)
Guardian Angel --> If you find yourself getting killed too much this can be a good pick.
Lich Bane --> When your ability power gets up to 500+ this becomes a good choice for harassing and team fights as it will increase your overall DPS by alot.
Nashors Tooth --> If you think you need the cooldown reduction.
For ability build... Some may argue with me but...
13-15 Molten Shield
17-18 Molten Shield
The only thing that i may recommend is that you get molten Shield at lvl 4 so you can proc your stun more often.
As for play style, thats something you can't teach, you'l know if this build works for you if you try it.