League of Legends (LoL) Question: What to max with Corki?

Q because the poke damage (Autoattack + Q) is epic (the damage is quite the same as the E). For gatling gun you need to keep your enemy under sustained fire which barely happens because you're kiting as well.

R>Q>E>W

I agree with everyone who says max q first becausenot only will it do magic damage, but it gives you sight soo it can give you an advantage in lane from the sight. Hope this helps!

The reason people max Phosphorus Bomb first is because it gives Corki very strong trades in lane + burst and also, it deals magic damage. Gatling Gun works very well in mid-game fights when you have your Trinity Force, and it combines well with your Hextech Shrapnel Shells to completely deny armor; it also consumes too much mana so it can't be spammed in the early game plus it needs you to be in very close range and facing the enemies to use it to it's fully extent.