I'm no pro with Warwick but I feel like the times I've played with I've done well and understood how to build and work with him in ganks and team fights. My build is centered around being tanky and lasting the whole fight while putting out a surprising amount of damage. I will go over choices you can make according to the items and runes

Firstly I'd like to address the runes i use for Warwick. First off lets talk about the Quins. MS quins are THE best, they're the only runes that are always as strong no matter the level or situation. Really the only other option i can see for quins are attack speed quins, but in my build i take care of that with the reds. Next up is Reds, attack speed is the way to go because getting physical damage or armor pen wont help as much as getting attack speed. the reason this it is like that is because of WW's passive, that's why my build doesn't need wriggles. After your recurve bow you can jungle forever. Next is Yellows and Blues, both defensive stats that make you intensely tanky at early levels, just a plain good idea.

Secondly i will address some variations with the build. Boots are the first things that you can screw around with depending on who you are facing. look at the team you're facing and determine whether or not you'll need the tenacity, if they have little CC grab Ninja Tabi. secondly is a more late game build variation. The only other options i would use late game is trading out the Madred's Bloodrazor for Atma's Impaler. This gives you less attack speed late game, but arguably the same amount of damage. I would only make this switch if i still need to be more tanky.

Thirdly the masteries, my masteries are focused on jungling and the all around stats for Warwick. Ever since i started using these masteries for jungling I've used them on every other jungler, I believe it is the way to go. Plus the movement speed in utility fits together sooo nicely with the movement speed quins.

Warwick's early game gank are honestly just horrible, the only chance you have is with your red buff. I start wolves, blue, wraiths, wolves, red, wraiths, golems all the while looking for a lane that is pushed. I wouldn't recommend ganking a lane WITHOUT red if it isn't pushed. If they're getting screwed in there lane and help is needed, then by all means you should be there to help. Once you get your Wit's End and Spirit Visage you turn into a monster, it takes atleast 3 people to take you down, depending on the circumstances obviously. once you hit 6 everything becomes much easier. Mid could be your best bet at getting a kill with your ult. Mid is composed of high damage squishies which means that if the opponent is surpressed your mage can unload everything hes been trying to do. Its the perfect combination.