this is my very first build, i wanted to make this build, cause i see much gangplanks who try to poke early game, but then you will run out of mana really fast, i think its better to focus on mid/late game, cause then your poke does much damage.

START:
with crystalline flask + 3 hp pots + warding trinket

as gangplank you need to farm with your q (which gives extra gold at last hit) early game, mana pots are a must to constantly farm your q.

CORE:
avarice blade + tiamat + boots

avarice blade scales really well with your q, cause it gives 2 extra gold at last hit, the tiamat is for the extra clearing speed

FIRST COMPLETED ITEMS:
statik shiv + ninja tabi's + alacrity

when you have farmed your q enough, you need to buy statikk shiv, cause it will give you extra q damage,
you dont need the mercury threads, cause you've got your w, which clears all crowd control, ninja tabi's are a good replacement, alacrity scales really well with your active/passive movement speed buff that your e gives you.

THE GODLIKE ITEM:
infinity edge

infinity edge is a must-have for critters

EXTRA SUSTAIN:
ravenous hydra

finish your ravenous hydra for the lifesteal.

EXTRA TANKINESS:
iceborn gauntlet

scales really well with your ravenous hydra

LAST ITEM:
guardian angel

you got full offense items, so guardian angel is really good due to the rebirth, and it gives you a little more armor/magic resist.

SITUATIONAL:
trinity force

as said, tons of damage

last whisper

if the enemy laner is stacking armor from start, you can buy last whisper

frozen mallet

gives you a lot of hp and the slow is pretty good for catching up to people

banshee's veil

its more tanky, and the passive shield is pretty strong against ad casters, mages, and cc

randuin's omen

really good item, gives you armor and hp, the passive is strong against attackspeed-based champions, like yi and fiora

GROG SOAKED BLADE
your passive is really good to catch up to people, or to kite a annoying singed who runs at max speed. the DoT damage is good for a little bit of poke, and in the best cases it can kill your enemy who just escaped the standard q-kill

PARRLEY
this is your main/and only standard damage ability, max it first for the extra gold at last hits and damage. Also, his q gives mana back at last hit, thats why i recommend farming with q at early game.

REMOVE SCURVY
this is the annoying ability, it clears all cc and heals you, max it second for the sustain and cooldown.

RAISE MORALE
this ability is good for the passive and active attack damage and movement speed,
i think you need the sustain more, so max this last. you can get easy assists only by pressing your e.

CANNON BARRAGE
the ultimate, its a pretty good one. cause you can assist your teammates, by throwing your ult at a escape path. or when you see a fight breaks out at botlane,throw your ultimate to provide of damage/slow. ofc it can be used to stop the enemy pusher.

9x armor pen reds

strong for late game, where you need some penetration to put some damage on the tanks

9x armor yellows

the most toplaners are ad-based, so armor runes are pretty good, i dont have health yellows, but i think after the runes changes, these are better than armor yellows

9x crit chance blues

i understand you think its worthless to have 9x0.28% crit chance, maybe you could better just take magic resist blues. but with quint + blue runes you got 8.1% crit chance, its a difference with 5.6% crit chance, which is what you would have with only crit chance quints.

3x crit chance quints

its good for the early game, when your jungler ganks you. cause you got chance to deal more damage, which is really strong

i recommend 21/9/0 cause you need the damage for late game, and you dont need that much defense, because you have got your w, which clears all cc. you could consider the 3 points in meditation for the extra mana regeneration.

gangplank is pretty good in splitpushing, cause he has itemwise some attack speed and of course attack damage, and his e gives him a attack damage buff.
also you can assist your team when they are engaged upon by throwing your ult to disengage/provide for damage and slow

+ got really high 1 target burst, with crit-q and statik shiv
+ got a good ult which can get you easy assists/kills and its pretty good to catch fleeing enemies
+ can carry pretty hard
+ so much fun to play

- really mana hungry early game
- pretty squishy when full offensive build
- if not farmed well, he is useless, cause he hasnt any hard cc
- can be countered hard by poke/non mana based champs/sustain