Thanks for looking at this build. This is a basic build that I tried and was surprised. Gangplank is a fun champion and I encourage people to play him. With this build you will destroy squishies and be able to survive in chaotic team fights. However Gangplank is a glass cannon and not meant for all players.

Pros
Huge damage
great fighter late game
global damaging ult
fast
Cons
glass cannon
nasty chest hair

My runes are armor pen, mana regen, and magic resist. The Desolation Quints and Desolation Marks are the only runes that you need to have. The others are flexible. I personally like the mana regen so I can use my abilities fairly regularly without getting mana hungry. The magic resist I have because It gives a small amount of protection against casters, especially off tank casters like nunu who focus on AP items only and not magic pen.

Max Parrrley first to gain the gold/damage bonus. Next I like to get remove scurvy for the heal. You can even cast when silenced so it is a heal that you can count on. Next get your E. Some like to rank their E before W because of the damage boost given, I haven't seen great damage increase from using this technique and rather have the nice heal handy.

At first start out with a Dorans shield. Great starting item that gives a small amount survivability. Buy two avarice blades so that you can get some gold and focus more on harrassing and less on farming minions. Also the 24% crit chance +3% from runes gives a nice chance to get a lucky crit on an enemy champ laning against you. Get boots of swiftness to give you the movement speed to go in shoot and get out or chase/flee effectively. Adding this to your passive effects of Raise Moral (e) gives you great movement speed. Sell your dorans shield to get your last avarice blade. Then farm/get kills until you can buy an infinity edge flat. Keep buying items flat until you need to buy a bloodthirster. You can buy the B.F. sword, then finish the recipe. I preferred getting a warmogs over any other item because I found that once I started hitting the enemy I could survive with the lifesteal, crit, and attack speed from the other items, but I was so squishy that it was hard for me to get into the fight without getting focused down even when my tank initiated.

Harass! Parrrley is your harassment move, and your passive is great way to annoy the enemy team. Also do not be afraid to use parrrley on a minion. I prefer to use it on one minion per wave or so, depending on my mana and the other champions aggression or health. Due to a recent nerf you can no longer deny, but your E still gives great attack benefit so use it before a harassing parrrley shot. Once you get your ult have map awareness, you can pick up some great kills with a well placed ult during a lane fight or even on a fleeing opponent. Laning with a champion that has a stun is optimal because they can snare them in your ult maximizing its damage. Remember that your W removes everything, stuns, snares, silence, everything. Don't take unnecessary damage because you don't want to "waste" you w. You can use it again in 30 seconds... not that long a wait.

Do not run into a group alone. You are not Rambo, you are a pirate. All you have to use is a rusty sword and a gun with one shot that takes 5 seconds to reload. only later game when you get your bloodthirter can you go 1v2/1v1 depending on the amount the other team fed you. I usually get fed nicely early game because of my teammate. Get a stun lanning partner and make sure you coordinate your focus. Also you should focus on a squishy caster that you can sit on with two hits and a parrrley shot.

Thanks for reading my first build, should be more on the way. Rate and comment to let me know how it goes for you.