M.Pen marks because ap poppy's sources of damage, namely DFG, heroic charge, and devastating blow are all magic damage.
Dodge seals are chosen because it can negate lots of damage from ad carries late game.
Health or armour seals do not synergise as well with her passive, however these are still good choices.
Glyphs can be chosen based on your preference, however in my opinion Magic resist, ap per level or M.Pen are best on poppy. Cooldown reduction glyphs are not considered because with full build you will be able to achieve 39% cdr. and 40 cdr with the elixir of brilliance.
MS quintessences for chasing and running.

Ignite after ult to get 40 percent bonus damage, can be used as soon as you get your ult off for healing reduction, if there is no way for the target to heal, then ignite when he is around 500 health, this allows you to use the remaining time of your ult to escape for attack another champion, while ensuring the kill.

Ghost is good to get to position for a wall stun, and for chasing down enemies. You will most likely find it difficult to chase down an enemy that had ghosted, but with ghost yourself you can chase down anyone with Shurelya's Reverie active, summoner Ghost, MS quintessences, MS masteries, boots of swiftness, licebane's MS bonus and paragon of demacia.

Flash is good for positioning yourself for wall stuns, surprise enemies by the sudden close of distance, flash over the wall to escape or following someone that had flashed over the wall. However sometimes you may not be able to catch someone that's fast enough, and that the duration of summoner spell Ghost allows you to be able to catch up to multiple enemies, which Flash does not allow.

Get sapphire cystal at spawn to allow yourself to cast more spells during laning phase, more importantly you will have gold to buy 2 health potions which enables you to gain lane dominance easier.

Poppy is great for bottom 2v2 lane, control the brushes at the side and look for opportunities to slam them into the wall and q, this combo would take a significant portion of their hp. Do not push lane and only last hitting would allow you to easily zone your opponents out of exp range. If the lane is push to them, wait for tower to clear your minions and repeat above steps. However you should avoid overextending, so make the enemy minions to push to your side of the map, this allow for easier zoning too.

You should go back after getting 1150 gold to get tier 1 boots and a philo stone. If you are not doing well, get health potions above boots, and get the regrowth pendent for easier laning.

Getting 2 philo stones is important for poppy, the reasoning behind it is obvious to any poppy player, however getting anymore stones would make you not do enough damage in the mid game, so 2 philo stones is a good balance.

getting kage's lucky pick is a personal preference, you can get sheen first then components of DFG, or if you need MS a lot get merc tread or swiftness boots after sheen.

Get 1 or 2 wards in your inventory at all times, these can be used to stop powerball if you are playing against rammus, or if enemies runs into brush, put a ward inside it instead of facechecking it, and slam your enemies into the wall finishing them off. Plus these can be used to prevent ganks from junglers or champions in general.

Any constructive criticisms are welcomed, and apologies for any error in language.