About me: Hello Summoners, my name is Impersonal, a filthy Normie from the realms of Summoners Rift. I've been playing Annie ever since I started playing League, literally Level 1, with that being said, I know a few things... I think.

Flash is pretty essential in my opinion, definitely something you should take.
I personally take Teleport more ever since Thunderlords was added, normally I can get enough damage off with Thunderlords to kill my opponent, also it's nice for map presence and tends to be a safe summoner spell to take.
Ignite is a good summoner spell in a lane where you've got a good chance of winning and are looking to get kills early, but with Thunderlords it might not be necessary to ignite all the time.

With Annie in lane I tend to play more like a dive bomber, if possible I'll walk within Q range with stun up and Q-W-Auto (for Thunderlords proc) then walk back, I try and do this quickly so my opponent can't attack back after the stun. IF THE OPPONENT STAYS BACK WHEN YOU HAVE STUN Keep your passive at 3 stacks and have 1 point at least into E, then walk into Q range and Q, while your Q is in the air press E, this will trigger your stun and it will stun the enemy when your Q hits, then finish the rotation of damage however much you can put out.

Annie's Q has a reset built into it, if Annie's Q kills a unit, the cooldown is cut in half and the mana is refunded, which is great for sustaining in lane and getting CS. However you should always still be able to last hit without using Annie's Q in case you're trying to keep stacks of your passive. Knowing how to zone your opponent off CS is also good, but depending on the matchup you might not be able to do that.

Whats gonna work? Team work
Annie can be great in team fights, with her ability to stun and 2 AOE abilities. If the enemy is in a tight space and grouped, Ult+W can do tons to change a teamfight, or initiate. Having flash+ult can be super vital for getting picks, or engaging/disengaging.

PROS

+Fun to play while ahead
+Relatively easy to learn
+Watching your opponents flash away from a Q at 20hp

CONS

Sometimes you'll loose, like on any champion
Annie's matchups can be a pain, especially vs long range poke champions.

Knowing these tricks will give you a very nice advantage over players who might not know these tricks.
For starters knowing that you can control Tibbers by pressing R when he's already casted allows the summoner to move him, you can use this to hold waves, Tank dragon, or provide vision in a bush while you recall if you're afraid of a surprise attack, with that being said, Tibbers is the real MVP.
Another really important/nice trick is having 3 stacks of Annie's passive up, then Q'ing and pressing E before your Q connects with your opponent for a surprise stun, this can be great for surprising your opponents.

If you'd like to ask me anything or see me play Annie, you can check out my stream Here. I'd be glad to answer any questions you might have about Annie or the matchups, etc. I hope you enjoyed this guide, this is the first ever guide I've wrote for a champion.