Crit chance is actually very bad on Warwick.

Because Warwick has pretty horrible synergy in some ways but awesome synergy in others its important to push what works.

For your Red, I would suggest Attack Speed or Armor Penetration. I personally use Armor Penetration for the extra damage, but attack speed will allow you to go with a different item build to get to the attack speed cap.

For yellow, dodge is a fair choice, it can end up being extremely good if you can get ninja tabi (which I may be doing myself now that his ult no longer leaves him open). I run armor in the slot right now because a Warwick with defense is extremely hard to kill in most situations.

For Blue, go off max for more attack speed or armor pen. You might also want to try using Magic Resist, for the longest time I was running Armor and Magic Resist and it definitely helped the early game fights/jungle.

For quints, I have discovered the joy of Run Speed, which helps you keep ground while your waiting for Blood Scent to activate (I've noticed with the fancy new graphics that it can take like 3 seconds before it activates)

For runes you should stick to what the mister above me stated. ^
For ingame items; I, myself usually go for:

Malady - Sweet lifesteal early game while jungling, also adds a bit of dps for each hit you deal to the target > While you're ulting them you'll raise your next incoming hits meanwhile and after your ulti ends.

Madred's bloodrazor - Attack speed, armor and 4% of the opponents HP in magic damage which means that your ulti will deal another 4% of the opponents HP in damage each hit. The bloodrazor needs a Madred's razor to be built, which also is very helpfull while jungling.

Wit's end - Effective against mana users, your ulti will hit for another 40 damage to all of the targets who uses mana. It's also usefull after ulting ofcourse.

Bloodthirster's - Lots of damage and lifesteal, combined with WW's passive lifesteal, it gives him a very good lifesteal in overall.

I myself never tried this, but some warwicks actually go for Sunfire cape's for survivability.

My build is -
-----------------
Bloodrazor
Attack speed boots
black cleaver
Phage
bloodthirster x2
-----------------
You will have about 2.0 attack speed with hunters call up, thats all your dmg +8% their max hp/second.
start off fights with hunters call + auto atk, hungerying strike if they get low hp, and save infinite durress for if you need a big burst of hp or if they run(most people open with it, thats bad idea).

If you master playing him this way, you can beat anyone 1v1

madreds razor, boots1, bloodrazor, mercthreads, sunfire x2 or Banshees and Sunfire, GA.

Bro. Attack speed is the only way to go. You become a king. Your passive with massive attack speed makes you godly.

-Attack speed boots
-Malady
-Wit's end (if there is mages, if not, Last Whisper)
-Madreds Blood Razor
-Sword of the Divine
-Black Cleaver

Thats my build. Configure what you wish.

For your build would it be better to get sorcerers shoes, because magic resist lowers bloodrazers effect, so instead of 8% per sec its around 5%, but with sorc you'll have about 1.8 attack speed, but maybe edging the the percent to 6% from the magic pen. although, now that i look at your build it has alot more AD then AP :P haha.

Would you suggest a half AP build with WW stacking things like malady wits and madreds? to proc WWs ult???

Also whats the phage for?, is it going to be built into the mallet?

depends i've seen some ppl build him with the usual dps carry build phantom dancer infinity edge blood thister ect ect.
but the buiild that usually works best for me is items that proc on hit since he's more based on attack speed plus these items are alot cheaper then the dps carry builds.
i usually get
-boots of swiftness
-wit's end
-madred bloodrazor
-spirit visage
-frozen mallet
-banishee's veil
the mallet and veil are situational usually u should swap if there's like say a yi xin and tynr on the enemy team to a tornmail. plus usually by the time u get the first 4 items the game's more or less over. but these are the items this is the build i usually use get madred razors > boots > wit's end> upgrade razors to blood razor > then get the spirit visage. btw u'll be very very tanky by the time the game ends

I dislike any build with Bloodrazer on it unless the opposing team is full of AD bruisers with low MR. That is the only situation I would actually get Bloodrazer.

WW is one of the most versatile champion in the game. And no, its not like Shaco building AP versatile. So there is never a "best" build for WW since one build would be better than the other in a certain situation.