I won't discuss here much about how to play ww - you can find such intel in other, more sophisticated guides.

I do have some experience with Warwick, checked few 70%+ rated builds and I can ensure you that this build is the best choice for Linewick. Some players argue about Warwick's suitability on the line - big mistake, ww is useful everywhere. Mid, solo top, bot - you can always score few kills with harassing (q spam) and when the enemy is below 30% health - ult->q->ignite->chaaaasing to make another q->flash from tower's range.
My build makes you very tanky, almost unkillable (great healing with increased durability) and allows you to initiate teamfights against not hard cc'd teams when somebody stays too ahead of his team (unless you have a better initiator in your team - leave it to pure tanks; you can initiate, but it's better to save your ult for nuker or carry).
Shortly about two last items. Pick Bloodrazor as 6'th item against tanky teams with lots of health, pick Frozen Mallet against fast, squishy and dps teams. You can always buy both of them in a very late game - as Doran's should be sold long time ago, sell Chalice, but be aware of your mana - ww without mana is ww without q what makes you an easy target.
Try it, rate it, tell me what should be changed.
Good luck, be fast and unpredictable! :)