AD Corki Mid - Win every single matchup

This item is VERY strong - to the point where I can't think of a single instance where you don't start this item.

NOTE: Doran's Blade's passive is now stackable, so depending on the matchup/reset timers it is encouraged to buy multiple of these (although, not more than 3 are recommended).

All my homies love Sheen.

In 99% of games, this is what you will be rushing as your first component. Very few champions are able to beat Corki in a short trade when he has this item, since AA + Q does a lot of damage and is both nearly impossible to dodge and non-committal. To get the most out of Sheen, I recommend using your auto attack and then instantaneously using your Q, which will make your initial auto attack use the Sheen proc.

Your second component should be Phage, since Zeal comparatively does not provide much value in most cases. There are some instances where you might consider rushing Phage before Sheen, but I would only do that in situations where you need the survivability it provides (usually if you are losing lane, and just need to coast).

After you finish Trinity Force you have a few options, primarily between Infinity Edge and Phantom Dancer. Since you are usually weaving abilities like Phosphorus Bomb (Q) and Missile Barrage (R) between auto attacks, I think the raw AD from Infinity Edge is more valuable than the attack speed from Phantom Dancer, but both are decent options. I have seen some people have success with The Bloodthirster as their second item, but I think crit is too valuable to give up on.

For your third item you can go Infinity Edge/Phantom Dancer OR Last Whisper depending on which item you went second, and whether or not enemy is buying armor. Last Whisper can be worth buying even if the enemy is not stacking armor, since it is both cheap and very strong in general.

For boots I have two potentially controversial takes:

1) Sitting on tier 1 boots (325g) and NOT upgrading them is usually the best idea, and there are a few reasons for this:
First of all, while the upgrades to boots are definitely strong, Corki spikes unbelievable hard with Sheen , especially in lane for short trades. As a result, I would prioritize finishing Sheen before upgrading my boots (sometimes even waiting until AFTER Trinity Force has been completed)

2) Sorcerer's Shoes are overrated on Corki:
It is true that a large chunk of Corki's DPS comes from his abilities, but it's easy to undervalue how much of it comes from auto attacks aswell. Sorcerer's Shoes makes his abilities stronger, but don't do anything for his auto attacks. Generally, my theory is that champions who aren't super reliant on one specific boot should generally go defensive, since they are an easy way to become more beefy without giving away valuable damage stats in your core build.

It is important to note, however, that if you do not believe that either Mercury's Treads or Ninja Tabi will be valuable, then I think Sorcerer's Shoes are your best option.

The following items are flex items, meaning they are only worth buying in certain instances.

I want to spend some time explaining Vampiric Scepter, since it requires an explanation. I consider it an in-between item, meaning it's a good purchase while you are in-between major item purchases. In League Classic there is a lot of AOE and other random damage that can chunk you out before or even during a fight, and for 800g you can use the life steal to keep yourself at 100% HP for fights. If you are stacking Doran's Blade's however, then you don't need the life steal as much.

The rest are pretty self-explanatory: The Bloodthirster to upgrade the Vampiric Scepter, Quicksilver Sash against heavy CC, Guardian Angel for a revive in the late game and Banshee's Veil since it heavily counters specific abilities such as Unstoppable Force (R), Rocket Grab (Q), Cryptic Gaze (Q), etc.