1. sapphire crystal + 2 pots
2. boots + catalyst
3. sorc boots + blasting wand or finish roa
4. finish item you didn't get + haunting guise pieces (i prefer ruby crystal)
5. finish haunting guise
This start will take advantage of Annie's biggest strength, her ability to crush most champions early game. Once you have these pieces in place, you have options, think like a tank at this point:
Are they building to counter you? Get your void staff, sell sorc shoes, and get merc treads. Then grab the hourglass and abyssal scepter. You are now a very tanky, can initiate, and will deal decent damage.
Are you crushing and showing no signs of stopping? Get rylai's fast, then build your hat and continue crushing. Careful, you're public enemy number one.
Are you doing just ok? Rylai's will give you some added utility and survivability, you may want to switch out your sorc shoes for boots of swiftness and get an aura item such as aegis, then continue building on your AP.
I use a rune and mastery set built more to my playstyle. mpen marks, mp5/lvl seals, MR/lvl glyphs, and move speed quints combined with a 9/21/0 (strength of spirit, not dodge) mastery setup. My summoner spells are unimproved ignite and flash.
For skilling order, I go Q, W, W, Q, W, R, E then prioritize R - W - Q - E .
Annie is a one trick pony and everyone knows it. Don't bother waiting for your stun to harass. Use your autoattacks to poke at them while you farm with Q. Once in a while, just jump in there and combo them unexpectedly, I promise you they will run. Many times, your stun will come up as you're comboing, flash after them, drop your bear on their head and net your kill.