Poppy is an AP tank(look her status),melle champion which invloves tons of damge and a very high ressistance.

First take your Q.
Q will give poppy a large amount of bonus magic damage for one hit,I think that many people make Poppy an AD tank instead of an AP Tank because of her Q and W skills which give her bonus magic damage not physical damage,of course that she may deal more damage from her basic attacks if she is AD,but as an AP,thanks to her Q's very short cooldown she will deal tons of damage,even more damage than you think.
I was playing a Co-op vs Ai game with Poppy AP and i was taking 50% hp only with the Q.
Maximizing Q is very important because she will have a shorter cooldown and lower mana cost.
Never waste your W,but farm with it cuz you will receive stacks that give you advantages on 1v1 fights,you can also use it to escape,cuz it gives you bonus movement speed.
Poppy's combo is Q-E-W-R,watch out when you are using your ultimate cuz you may waste it use on a target which you are sure that you can kill it,you can also use your ulti to tank the turrets applying it on an enemy champion.
If you want you can take the red buff to slow your enemies while trying to kill them.

If you want to fight against or along with me i am Costel773,EUNE.
Gl and Hf