This build is something I came up with while messing around with different GP strats, and I found that you can absolutely clap matchups with this setup. I've had pretty good success in mid and top, and still have the kind of damage you'd expect from regular GP. In the Chapters we'll go over the items, runes, abilities, Pros/Cons and the different phases of the game.

-Tons Of Damage: GP normally does a lot of damage, and this build doesn't stray from that path. We get a solid amount of Lethality for squishies while still maintaining a healthy amount of crit chance. With GP's new Barrels this combination is DEADLY.

-Built in Escape: Duskblade passive makes it so you can get a kill in a teamfight and then use that time when you're invisible to reposition or get out before you get blown up.

-Bad Early Mana: This is less specifically the build, and more so just GP in general. Regardless of what he builds he will always have mana issues pre level 6.
-No Mobility: Aside from Mana issues, Gangplanks other big problem is his lack of mobility. There are technically ways to resolve this like Galeforce or Prowlers Claw, but Galeforce doesn't really fit on Gangplank and while Prowlers Claw is great for his damage, the mobility feels janky ever since they got rid of its ability to click to minions. Just use Duskblade passive and reposition in fights when possible.

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  Innate: Gangplank periodically empowers his next auto with a burn effect, dealing true damage to the next enemy hit over 2.5 seconds. It scales with bonus AD and has a 15 second cooldown. For each successful hit with Trial By Fire, Gangplank gains bonus movement speed for 2 seconds. Trial By Fire's cooldown is reset every time Gangplank blows up a Powder Keg.
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  Active: Gangplank shoots an enemy with his gun, dealing physical damage, and applying both on-hit and on-attack effects at 100% effectiveness as it counts as a ranged attack. Parrrley can crit and is effected by Infinity Edge's crit modifier. If an enemy is killed by Parrrley, Gangplank gets bonus gold, and gains Silver Serpents, which can be used to upgrade Cannon Barrage. If an enemy is killed by a barrel that was set off by Parrrley, Gangplank also gains bonus gold and Silver Serpents.
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  Active: Gangplank consumes **** tons of oranges, cleansing himself of all crowd control effects and healing himself.
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  Active: Gangplank starts with 3 maximum barrels, increasing to 4 at rank 3 and 5 at max rank. Gangplank will also stock up on barrels up to the current maximum. Each barrel has 3 hp and over time the barrels will lose hp until they are down to 1. The time it takes for the barrels to decrease to 1 hp will decrease at level 7, and then further at level 13. Once a barrel hits 1 hp it is now able to be set off by Gangplank or defused by an enemy. Gangplank's Barrels can overlap as long as their radius' are touching. If there are barrels connected, destroying one barrel will trigger the others on a slight delay. Barrels can be activated by auto attacks or Parrrley. Enemies hit by the explosions are slowed for 2 seconds, and have 40% of their armor ignored. If the auto or Parrrley that triggers the barrel is a crit, the barrel explosion will deal 25% more damage on top of the crit damage. Each enemy can only be damaged once per barrel chain.
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  Active: Gangplank calls upon his ship to fire a total of 12 waves of cannonballs, in clusters of 3, every 2 seconds for 8 seconds total. Each wave deals magic damage and slows enemies by 30% for .5 seconds. Gangplank can also purchase upgrades for this ability once he reaches 500 Silver Serpents. This ability is global, meaning it can be launched at any spot in the map.
  
  A large cannonball strikes the middle of the ultimate after the first cluster, dealing true damage to enemies hit in the center of the ultimate, and slowing them by 60% for 1.5 seconds.
  
  An additional 6 waves(2 clusters) are fired over the duration of the ultimate for a total of 18 waves in clusters of 3 every 1.33 seconds.
  
  Cannon Barrage grants Gangplank and his team 2 seconds of 30% bonus movement speed whenever they enter the ultimate's radius.

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  First Strike is an especially effective keystone on Gangplank as he counts as a melee character, gaining full usage from First Strike, but he can still hit his enemies from a distance with Q and barrels.
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  Perfect Timing is just a free stopwatch. There's nothing else to say about it.
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  Minion Dematerializer will mostly be used so you can blow up waves with barrels sooner and more effectively to get the most of your silver serpents. Which in turn will allow you to get the upgrades sooner.
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  Cosmic Insight will get your flash up sooner since you have no mobility as Gangplank.
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  Since our barrels slow enemies, this will increase damage after so if the barrels dont kill them, the next attack will.
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  money.
  Secondary Runes
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  Dark Harvest is a lesser used keystone on Gangplank, but is still good for those who want something other than Grasp or Conqueror. It's incredibly easy to get stacks as Gangplank as your Q is point and click, your R is a massive global circle of cannonballs that allow you to be involved with any fight at any time across the map. The amount of stacks you're able to get could range anywhere from 20 to 50 depending on how ahead you are, and how involved you are with your Ultimate.
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  Cheap shot will be good for damage after the initial sucker punch. Seeing as cheap shot will activate after both E and R, you can Barrel chain or ultimate a team, walk up, and deal bonus true damage to any enemy of your choosing.
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  Eyeball Collection is good for the Permanent AD as it'll help you scale up during mid game.
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  Ultimate Hunter will lower the cooldown of R for every takedown you get. This will be great, since your R can be extremely impactful in a teamfight, for taking objectives, or even just getting your team out of a bad spot.
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  Manaflow Band is going to be our early game help for building up your mana pool.
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  Gathering Storm is going to be the brother of Eyeball Collection, and add even more Permanent AD to scale you into mid game and late game. With this you can have 80% crit, and go into late game with an unhealthy amount of AD. Together all 3 combine for a one shotting machine whose only purpose is to delete anything with less than 3000 hp.

Essence Reaver is our first item because it gives us crit, AD, it's cheap, and most importantly, it gives us a Sheen Proc. What makes that so important is that there are only 4 items in the game that build a sheen. 2 are mythics, 1 is an AP item, and the last one is Essence Reaver. We essentially hedge our bets with this by getting a sheen proc without needing to hinder ourselves by putting that sheen into one of the mythic options.

Duskblade of Draktharr will be our mythic because not only is it one of the cheaper AD mythics in the game, but it gives us tons of AD and lethality as well as camouflage after takedowns which will be great for teamfights and skirmishes. Since we're getting Essence Reaver first item it also won't feel as bad because we'll have a little bit of crit chance built up early. It also has a damage boost attached to it which makes our already incredible damage, even more incredible.

I like Ionian Boots of Lucidity, as it helps with your R cooldown and having your abilities up sooner is always going to be better. They're also pretty cheap for boots, so they help with gold efficiency. Though the boots can vary based on what's needed for a matchup.

Lord Dominik's Regards is one of Gangplanks best items because he's generally a squishy champion and we don't buy health items on him. It's not terribly high cost and since we already blow up squishies, this item is best used against bruisers and tanks since they're always going to be harder to kill. Even if the enemy comp isn't incredibly tanky this is still a good purchase for the armor penetration and the crit chance, because the other armor penetration legendary doesn't give crit chance.

Mortal Reminder is a cheap but effective anti-heal item for marksmen and crit users that Gangplank can also use. It's a good item during the transition into late game and if ahead will make it a lot easier to buy Infinity Edge later because we're not spending 3000+ gold on our 5th legendary. Obviously it's best used into healing comps, but even if they don't have much healing it's still a good item for crit builds because of how cheap it is.

Infinity Edge will be our last item as it gives the most AD by a legendary in the game, adds more crit, and makes your crits deal more damage, which applies to your Q and E. Since we have 80% crit we can use this passive more effectively. You won't get to this point every game because the item is costly and you can't be 10/5 every game, but when you do get it, Infinity Edge is an incredibly fun item on Gangplank.

Early Game you'll want to focus on farming, and occasionally poking your enemy down. Try to save your passive for trades if you can get a quick and easy auto on your enemy. Once you get enough gold for sheen you can either shove the wave in and back or try to go for an all in if you're in a favorable setup. On first back be sure to buy your Sheen and get back to farming. Once you hit level 6 be mindful of the other lanes so you can get some easy assists and dark harvest stacks when possible(if you're running the secondary page). You can also use your Ultimate to contest objectives and possibly force the jungler off. The sooner we can get Ultimate the sooner we can get involved in fights and turn the game to our favor.

By now we're past laning phase so you can either continue pushing down lane and then group after 2nd tower, or you can start roaming to open up other lanes and get more dark harvest stacks(again, if you're running that rune page). Either direction you go, you should be set to turn into a powerhouse as you'll already have your level 7 powerspike and be close to your level 13 powerspike. Try not to get too cocky though as you're still as squishy as ever and one misplay can lead to you getting wiped off the map.

At this point you should be grouped with your team, and have one Ultimate Upgrade. The Ultimate upgrade you choose can depend on your own playstyle and the needs of your team but for the most part I usually go with Death's Daughter to try and force one or two people out of the fight immediately. After that I go Fire At Will for the additional waves which should help secure kills, and then finally Raise Morale for the rare chance you'll actually need the movement speed. Finally, focus on getting to Infinity Edge and being involved in the teamfights you can be impactful in.

In Conclusion, This build is about winning the mid game, opening up other lanes, and building up your power through your keystone and your natural power spikes. Whether that's by cutting off the enemy bot lane to give your ADC a double kill, contesting an important dragon to force the jungler off, or just by beating the **** out of your opposing laner. It's a lot of fun and has a nice additional touch that I feel escalates Gangplank above all the other champions. Hopefully you enjoy the build as much as I do. GLHF!