I recall a few 5v5 and 4v4 ARAMs with all Bro12ers.
Anyways, Poppy wall of text promised:
First, let's get some information for everybody's sake out of the way.
Passive: Halves damage over 10% of your HP, and only the portion over 10%.
Q: Does AP damage equal to Autoattack (Including Crit), in addition to 100 (+.6 of AP) and 8% of the target's max hp, capped at 375 (Around 4700 HP) CD is 4 seconds (2.4 with 40% CDR) It's supposed to include other damage bonuses as AP damage (Sheen, TF, Lich Bane) but it's bugged and works inconsistently if ever.
W: Passively grants 3.5 AD and Armor each time you damage an enemy or take damage, max 10 stacks, stacks last 5 seconds. Active grants max stacks and 25% bonus MS for 5 seconds.
E: Charges to a taget and then pushes them about half the max range further. Targets take 150 (+.4 of AP) AP damage, or 425 (+.8 of AP) AP damage if they hit a wall. Targets hit b a wall are stunned for 1.5 seconds. CD is 8 seconds (4.8 with 40% CDR). Poppy can charge through small walls if she has vision, but can't stun enemies on created terrain like Anivia's W,
R: Can only be damaged by 1 enemy champion for 8 seconds and Poppy does 40% bonus damage to the target for the duration.
With that out of the way, the 3 playstyles for Poppy are AD based, AP based, and a hybrid of those. She can jungle, or top lane, as well as go in a kill lane bot or mid.
Most Poppies will max Q first, but some will max W first with an AD build.
Poppy tends to play either super aggressive during laning in hopes of getting early kills and snowballing off of that, or playing defensive and trying to farm through laning phase. The former is more likely on match-ups that favor Poppy.
Champions with true damage are the most effective counters to Poppy (Olaf, Darius, Irelia) while champions who can safely harass her outside of her range can do well (Ezreal, Swain, Caitlyn), and champions who can manage to survive her burst in lane until she runs out of mana can avoid feeding her. Recommended counters: Olaf, Darius, Vayne.
Poppy likes to combo E into Autoattack reset+Q in lane if she thinks she can pin you, and then run back while she waits for cooldowns and another good chance to strike. If she doesn't stun you, now is best chance to engage on her. If you do, she'll either get hurt massively, or be forced to use her W to run away, which will shred her mana pool very quickly.
AP Poppy does a metric fuckton of burst damage. There's not getting around that. Once she gets DFG and another big AP item (Zhonya's or Rabadons usually) one of your squishies is a dead wo/man walking every 100 seconds. There's no getting around that. However, once she uses her burst she's completely useless for the next 10 seconds or so, and she won't have the same WTFBBQ killing power for another couple minutes, as she doesn't have the CD resets or super short CDs most assassins have. Until she gets her first few items, AP Poppy is probably the weakest way to build her. Lanes with her tend to have a lot of killing, for both sides.
AD Poppy does a ton of sustained damage, and is absolutely insane to kill. She also likes to ult the tank or support rather than carries, so she can get free picks for the 8 seconds ult lasts. AD Poppy can max W over Q and then absolutely crush most lanes, due to the massive armor boost. AD Poppy is weakest during mid game, unless she gets fed during laning.
Hybrid Poppy likes to build a mix of damage, and will do around half and half damage, and still get quite tanky. She's an absolute monster through most of the game, but suffers from having expensive build options, and if starved is very little of a threat. When fed, however, this is the Poppy that scores Pentakills.
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Ok, now for opinionated stuff.
AP Poppy is one of the worst assassin picks you could possibly make. Assassins like Akali and Katarina get cd resets for a reason. Their teamfight presence would be immeasurably lower without it. Once Poppy blows her burst, she's done, teamfight's down to a 4v4 and there's not really a whole lot you can do. The reason I compare her to Veigar, is because that's pretty much what he does too. He absolutely erases one target, and then would be useless, were it not for the fact a portion of his burst is AoE, and that ridiculous instant AoE stun. Another advantage Veigar or other assassin have over AP Poppy are decent AP ratios. She has an AMAZING 1.96 AP ratio before extra AP ratios like DFG and Lich Bane (Ok, I'll grant you she gets slightly more out of those than other champs because of her ult amplification, but still.) That's absolutely abysmal.
Let me say this again, so we're clear.
She doesn't even get 2 damage per point of AP. When she uses her ult. She gets more than that with AD burst (AA + Q).
Sorc Shoes are certainly a must on AP Poppy, because she already scales so little you don't want that scaling mitigated by the fact every single champ already gets 25% built in damage reduction to her.
Sorc Shoes are not a must by any stretch of the imagination on anything else because almost every other boot is so much more useful.
[/ap poppy hate]
Ok, now I've had my say and there's nothing data vampires can do to stop it. I can move on now.
Teemo you say? My personal favorite tactic is to max W on him and then just afk push the lane then use it to run every time the jungle shows his ugly mug, but that's not really a pro tactic, so more serious advice would be to keep shroom ammo pile empty as much as you possibly can. It's all right to miss a few cs if it means you can shroom half the map. If your pile hits 3 shrooms go somewhere else immediately and put some shrooms down.