Gangplank(GP) is realy kind, I played GP many times as every of these roles, probably the best one is a solo top becouse you can carry all the game alone, if you can feed yourself and farm minions. The best choice how to start playing GP is probably solo top too. Many people are think that GP is low and can be countered by everything, but that's actually not true.
GP is mostly played as tank in jungle(GP as Jungle) but if you are tank and you are not fed you can't do any dmg and that's it why we play him, GP can be realy aggressive from early game and one shoot killer in late game, With 400 dmg and trinity force you can crit unarmored enemy with crit about 1800 and it's like ad carry without defense items. My biggest crit I ever did in ranked game, was with 360 minions and score 9:0:11, It was 1608 to oriana without defense items, I got shield from janna (+50 dmg) and Raise morale, and thats all without trinity force, if I had it I think that crit would be more than 2000. And it's pretty nice. I think that's all and now to the guides.

As solo top, I pick regrowth pendant for longer survival on line and that's becouse your enemy can be aggressive but if he takes boots you can just go back, and wait, until you get back your health and haras again, potion is for longer haras and probbably you will get first blood thanks to it. From the begining start haras with your parley until you get your enemy to half or lower hp (never use flash until enemy do) With armor pene runes and mana regen + crit runes you should be able to get enemy there in 3 minutes, if your enemy has big regen, dont use parley for haras, it won't be effective, use it for farm to overfarm your enemy, always try to last hits minions becouse you are easy to kill if you are ganged, when you got the kill or quite a lot of farm go back and buy some items I recomended on top you dont need boots at the begining you are quite fast even without them and better are gold items. With ur farming and gold items + maybe kills you can be able to get more than 5 k more gold than everyone.
When you back to line you should have about 20% crit is realy hard for enemy to stay against parley that crits 1 or 2 times from 5 parleys, the best choice how to kill enemy from 6 lvl is
a little harras then go for him (you should be faster thanks to raise morale) and you should use exhaust, when he flashes away use ur ulti at him and flash to him, yeah you got another kill, if your enemy escape(you have another chance in some minutes. when you are under enemy tower, you can parley him without taking dmg from tower. when u got ur infinity edge(probably in less than 20 mins) you can gang easily every like, try to choose those, where are some squishi enemies, the best choice is support(lower hp, no def) you can crit them for 700 dmg and it's like half or more of their HP. you should be able to catch everybody with that 440 speed if not use ur ulti.
ulti - is GP realy strong weapon, if oyu are in base and your friends are ganged,, use it for help them to escape. Same way to use ur ulti is for killing enemies who escaped with 1 bar hp or something, if your team has cv use it where they can be and use ur ulti when they are recalling.
As next think you need some survivality, if your enemies are fed too buy warmog and atmas, it will give you about 3 k hp and armor + some dmg. On the other hand if your enemies are not fed you can buy bloodthirster and last whisper/trinity force. with these things you can instantly make your enemies to run away with low hp.!!Always choose enemies as support or ad/ap carry!! these are squishi and it'll still help you to win if you kill them.

As jungle you start with Raise morale on blue, take blue and:

1. You can continue to jungle, go wolves then golems(wraiths are too hard for u) then you cna go red or if you dont have hp go gang or back and return to red and complete jungle
2. You can gang top/bot (depends on your team base) early gangs are realy good for you becouse if you get kill, you have easy jungle becouse you can instantly buy razors, and enemy doesn't have ward. (this realy depends on your situation.

Most of the times if im jungler, im tank, and gp as tank is big dmg still, and you can just come from jungle and push tower and enemies can't do anything.
use your ulti to push lines or on minions that pushing your tower with enemy. this will give you a little farm + your towers can't be destroyed sometimes.
try to gang as many times as you can. if your enemy use flash to escape just go back to the jungle and come again. even if you are tank, you can do more dmg than many carries on lines. and good think about it is that you have more hp and armor than everyone.

Support is the most funny role as GP, everything you need to do is just stay in bush and parley your enemies everytime they come nearby. if you crit support as janna, she will get to half hp and your ad carry can easily kill her. and if you criting their ad carry he can't farm.
For items I buy more and more crits for criting enemies on line and sending them back to base many times. this will give to your ad carry free farm, or you can gang lines too.
Items those i have are support/tanky items with quite a lot of speed and crit for killing ad carry in late game or tank the whole fight. That's all about Support GP.

GP as ad carry is quite hard and its best to play him with soraka. With soraka you have free farm with parley thanks to infinite mana, and haras too. Items are same as every ad carry in the game, you have quite a lot of dmg and banshee in alte for surviving hard atacks as annie flash/stun combo or stuns. thanks to your ability remove scurvy you can easily survive 2 stuns in a row without taking dmg. as ad gp try to parley your enemies and stay behind team fights and when your enemies are low just jump there and kill them all. be carefull in early games, if your enemy is cait, you have hard farm so you should take him as ad carry just against some ad carries like ashe or something becouse its anti ashe carry.
Parley - parley can be used for better things than just haras. it can be used as antibanshee use it on enemy who have active banshee for let them easy to focus by your ap carry.

Just something about my friend. My friend have some runes for critical dmg% if he buys infinity edge, he crits minions about 1100 dmg. and this is just with one item. try to crit more with one item :)