Wild Corki appear :P
That's how I use to play my Corki. But well you all know that every game can go different because you don't face the same champions or you can find an ability power feed so you would need banshee or you can find a game with a dps feed, so you would need armor etc...

Well I use to pick this runes as "master".
Armor penetration about 10 points its okey, because Corki deals true dmg by 10% or something like that.
Critical strike damage : I think that's important because you can't incrase it in game, only infinity edge does it once and with this runes you hit 270% not 250% so that gives you advantage between other dps.
Mana regen: Well I like to play all my dps champions with mana regen, so I dont have to go back all the time when I run low in mana. Corki spends a lot of mana and you can be sure with this runes that you will never miss mana for ulty.
Magic Resist : Well that's not the most important you can switch it with other ones but I like to be "tanky" at first levels, so that helps me to take some dmg and don't die. Also my first item is cloth armor wich gives me armor and its all okey for botlane.

Well I like this ones. I hate slow champ move, I like to fly :P . Thats why i put 8 points on utility. Can't comment more for this. Only that if you play Corki without flash you can switch this orders and make some adjustments.

This build is a bit "Solotop" but works great on botlane too. If you don't want the lantern you can go for 3 daggers and you will go pretty good. But I like to have lantern because it helps you to farm much faster and helps on dragon or jungle (stealing blue or whatever) If you spend less time farming you win more time to move arround the map and join your teammates.
I used to watch a lot The Rain Man and that's why I got influenced by this build but well you can always make it different as I said on description. Every game is different and your build can be diferent. If you want to go strong damage on botlane I preffer to go with 3 daggers , boots and then go for infinity edge then zeal dancer and blood.

You can play without flash , but you have to be sure that you have mana for your W to escape. And you can go for teleport if you play on top lane. Also you can do Exhaust + Ignite for botlane, its op ;)