I usually like to start 3 health potions and a mana potion. The reason for this is because Warwick can easily get counter jungled if you start blue and go to red. Therefore, I start red and go to blue. Once you have gotten to blue, your mana will be dwindling so the mana potion comes in handy. Also, warwicks passive allows him to stay at full health the entire time between the first two buffs without loosing any health in the first place so the excess health potions are worthless. Getting blue second also ensures maximum mana efficiency from being able to have blue all the way up until level 5 which allows him to farm the jungle like a boss. Since warwicks ganks pre-6 aren't very strong to begin with, it is ideal to farm the jungle as long as you can, as long as your teammates have pushed their lanes during the time that you are farming. With warwicks main items (Feral flare, wits end, and blade of the ruined king) He WILL be able to kill ANY ADC with just one ult and use of the blade of the ruined king active ability. Getting spirit visage not only reduces the time of warwicks ult (as if it weren't short enough already) but it also gives massive lifesteal with warwicks passive and blade of the ruined king combined together, and adds a little tankyness to warwick. The frozen mallet adds some tankiness but more importantly makes it literally impossible to run away from warwick without using all of your summoner spells to escape.

Lets just get this clear. Warwick has a very small amount of counters. In my opinion he is a little unbalanced and with the right items he can literally 1v1 any champion in the game and still end up with close to, and if not, full HP. With the right items he can also kill ANY adc with just his ult (assuming the adc doesn't have cleanse or an item that allows them to get remove CC) I've gotten over 30 kills in a game with warwick and have an 80% win-rate with him out of more than 200 games.

I prefer damage oriented runes with warwick. Warwicks ult is really his bread and butter, and the damage runes help excel the damage of his ult and improves his jungle clear time massively. Warwick can be built as a tanky champion and therefore tanky runes are viable but as a Warwick player you want to rely on the damage and CC from his ult to carry your team to victory.

I prefer damage heavy masteries for the same reason I prefer damage runes. A good build with warwick will allow him to 1v1 any champion in the game and will also allows his ult to kill any enemy ADC from full health to 0 every single time his ults cooldown is up. It will also help his jungle clear time increase which means hitting level 6 faster, which means strong ganks.

PROS: Can 1v1 anyone, Can hold enemy player in place while your team beats on them, Can roam enemy jungle without being scared (after level 6), Can Kill any enemy adc with just one ult (assuming he has the correct items), Can easily melt tanks with blade of the ruined king and stacked attack speed, People don't tend to focus him since some people don't see him as a threat.

CONS: Weak pre 6, slow ganks pre 6, Only has really efficient ganks with his ult, Can't carry the team hard enough if they feed early game.

As warwick it is crucial to get your feral flare to 30 stacks as soon as possible, as this will greatly increase the damage of his ult (since he ult procs 5 auto attacks within the full duration). Since it is so important to rush feral flare, be sure to only gank when the enemy lanes have pushed your teammates lane and the gank seems like it would be an obvious kill. When you hit level 6 you want to gank as soon as possible. Continue to gank every single time your ult is up and try to use your ult as soon as it comes off cool down. Warwicks ult is basically a free kill. Treat it as such. Besides coming out just to ult someone and get a kill, continue to farm the jungle to rush 30 feral flare stacks as soon as possible. Since warwick is an item dependent champion it is important to farm the jungle as much as possible while still ganking every single time your ult comes off cool down.

Warwick is an item dependent champ. With no items or the wrong items, he is worthless. With the right items, he is the strongest champion in the game. After hundreds of games I have come up with the list of items that I think is the most overpower with him in this order. With this specific item set, your ult will kill any enemy adc. You will also be able to melt tanks in one on one fights and will be able to have massive amounts of lifesteal, which will keep warwick at constant full health, assuming you are in the jungle.
1. 3 health potions, 1 mana potion, jungle dagger
2. Claws
3. Feral Flare
4. Wits End
5. Blade of the Ruined King
6. Spirit visage
7. Frozen mallet