Umm - Ever since they nerfed Ar Pen, I always thought they were not quite worth the extra pen - imo, extra health would help with the early game, and if you really want to be aggressive, MS quints can give you the extra MS to position Heroic Charge.
With regards to early game advice, here's some of the tricks i used when i was playing poppy very seriously
1 [not quite as viable now], but i really liked to start with a fortify elixir, start a fight at very low levels, then jug a red elix when they commit for the kill. Given how your passive works, you should usually win those fights.
2 Combine teleport with an early ward [which, if you are going for a red elix, you will usually have] and ward one of the lower lane brush [ideally before minions spawn], and use it as a surprise initiate on brush huggers. Plus even w/o port, you can scout second brush, and flash + charge something into the wall. With port, farm agressively, then advertise the fact that you are going back with a blue pill. Teleport to the ward, then heroic charge into turret when they are pushing turret. Port + ward is also a very good anti-jungler strategy, esp. with poppy, because of her charge, and early burst [usually enough to finish off an early blue buff farmer].
3 - A very specific FB oriented strategy would involve pairing with a teemo with exhaust and ignite, have him rush to second brush and cloak you hide in first brush, wait for them to face check second brush, walk out casually then charge the squishies target. Between you and teemo, nothing with <500 HP will survive that.
At the build level well... if you want to well early, sheen is probably the only thing you've got right. Trinity edge only gives a substantial boost to damage once completed and costs a bloody lot to complete at that, while providing only marginal amounts of utility in between [even more marginal if you're popping points into W instead of Charge]. For shoes, regardless of AP, or AD, most of early game damage is going to be your Q anyway [besides, you still have the Mpen mastery, so it probably hits at least as hard as your AP cousin would do, if not more from having 21 offensive masteries], so you'll kick up your bursting potential significantly from having the 15% CD reduction on lucidity.
For your post sheen items, look for stuff that works well with your abilities inherently - For example, Gunblade nukes for a hell lot of damage on ulti, and will vamp massive amounts of HP on Q, while any combination of Ghostblade [CD + attack speed + armor pen + movespeed + crit], Rageblade [not that good on its own, but deals exponential damage when paired with armor/resist reducers], Malady and Black Cleaver form a range of relatively cheap, but very effective syncs, esp. since Ghosblade/Black Cleaver, the most expensive items here, are semi-luxuries.
Unlike AP poppy, who's damage boost on lich bane proc far outstrips her sheen proc, AD poppy can pretty much afford to upgrade sheen last.
Personally, I'd go - Sheen - Luci - Gunblade - Ghostblade - Malady - Black Cleaver - [Trinity], the general idea being that, even w/o ulti, your exponential damage growth, spammy burst, massive lifesteals means that very few things can fight you head on, while gunblade will still allow you to ulti and melt a priority target.
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