There is my build for Gangplank. I chose to max his Parrrley because I think it's his most powerful add useful skill.
Sheen : you need it. 100% more dmg on your next physical attack (parrrley is physical). When you use parrrley, sheen is activated and when the bullet reach the target sheen get used. In addition, sheen will provide you enought mana to do well.
Last whisper : 40% armor pen. I don't think I'll need to explain.
Ninja tabi : or mercury tread at your choice but don't take berserker greaves its useless, last whisper already give you attack speed.
Infinity edge : Of course
Avarice blades : for crit(24% for two) and money. Buy them early in the game.
If you have the money, sell avarice blades and get a Bloodthirster for lifesteal and damage. And finally, if the game is very long, banshee veil is always a good choice. Or if you really own, get black cleaver and the other team is done :P
When the game start, buy crit brawler and 2 health potion and put youself into harassing mode. Try to lane with a melee so you'll be able to avoid damage and do hit and run.
Don't waste your mana when you know it's useless to harasse.
Focus DPS: you you can burst to 650 damage at level 8 if you do well so on a teemo with 1100 HP It's kind of funny.
Use cannon barrage to defend towers.
Your remove scurvy is not only a heal that can save your life by removing CC. It allow you to feint you oppenent.
For exemple, you have 300/1300 HP and Teemo want you. You are staying around your tower and defending. Your remove scurvy is lvl 5 and can heal you for around 400 HP but you decide to wait. Suddently, teemo flash into your tower and try to kill you, he blind you and....HOOOO HEALING +400HP....BANG CRIT ON TEEMO. Teemo get killed by tower and you survive with 200 hp !