Well, I've asked this a few times and it seems like you can go AP or AD. The biggest core item for poppy is the sheen (and things that the sheen builds into) because it spikes damage every time you q, everything else varies on build.
AP poppy does dfg + ult to give her stupid high spike damage, and in this case you're going to get lich bane, dfg, deathcap, boots, and items to taste (rylai's, abyssal, Liandries, RoA, Voidstaff, warmogs, etc).
AD poppy will still murder someone with ult, but is built for more sustain damage and massive q's. My list for ad Poppy is trinity force, bloodthirster, infinity's edge, frozen mallet, boots, and warmogs. That list has good burst, good defences (w/passive), and can keep people within swinging distance.
I don't like to say focus on one item above all else, but the sheen really is killer on Poppy.
edit: masteries are usually 9/21/0 (for early game durability), but I've heard of 21/9/0 (for max burst). Runes that I use are gold flat armor, blue scaling magic resist, red AD, and movement speed quints. YMMV