I've seen many planks building some funny items and failing. I've the best success so far with this build. Gangplank doesn't need any offensive items at the beginning, so philo stones are the best choice for survivability, laning capability and harassing your opponents. Make sure you got crit chance runes so you should end up at 18% crit at lvl 1. That's enough for early game. Mid game with this build you should be able to parrley crit 1/2 hp of squishes. As Gangplank you are able to take on 1v1 any champion

Armor pen Marks / the rest critic chance

Start with 2x Faerie Charms and 3x Health pots. Build 2x Philosopher stones and boots. Now, the rest is situational, but I personally go with at least 1 Avarice Blade for extra crit chance and then BF sword. With philo stones you should be a farming god, so there shouldn't be a problem with getting Infinity Edge before 25 minutes.

I go with ghost and exhaust. Works great for both first blood and escaping.

Last hit creeps and deny whenever you have the skill ready. Your priority on denying is tank creep > melee creep > mage creeps. Last hit creeps with parrley once you have it on lvl 3 so you get decent extra gold. You should have 2x philo stones + boots at about 10 minute mark, then you can lane forever. Use your W when needed to get some health back.

make sure you parrley squishes as often as possible. I would suggest hit and run play style in teamfights, just make sure you target squishes and melee attack champions with healing/regeneration abilities to apply your passive. Just don't run into the opponent as you will die pretty fast, let the tanks take damage and take care of their squishes.