The Best Build I've been able to find for Warwick enjoy.

Pros:
He has good clear with Tiamat and Blood Hunt
Has good chasing potential
If played well good Team Fighter and Front Line
Good at disrupting the Enemy Team in Team Fights with good usage of [E] Primal Howl
Good sustain not only in Jungle but in Fights
Can do Early Drake solo with Double Buffs cause of his insane Sustain.
Good in 1v1 Scenarios

Cons:
Prone to CC
Prone to Kite
Easy to bait yourself with
If you miss your ult your Team Fighting Potential becomes a lot worse.

13.5% Attack Speed
8.5 AD
5% Flat CDR
4.9 Scaling CDR
4 Armor
120 Scaling Health Per Level.

13.5% To get targets under 50% for Fast Clear
8.5 AD For Clear
5% Flat CDR for Early Clear
5% Scaling for Late Game 40% CDR
4 Armor is all you need to stay healthy
120 Scaling HP for Late Game

Ferocity Tree
Fury: Because the Attack Speed feels nice
First Blood: Because it applies on Ult and Q
Natural Talent: Because he has both AD and AP Scaling Ratios on Q
Double-Edged Sword: Gives 5% more damage but makes you take 2.5% more damage it's worth the tradeoff
Battering Blows: You're AD obviously so the pen feels good.
Fervor of Battle: Because you get High Attack Speed on low health targets so the bonus AD feels really good when you're hammering low HP targets.

Cunning Tree
Savagery: For the extra 5 damage on autos for faster clear
Runic Affinity: For longer Red Buffs (Which applies to Q and Ult) and Blue Buffs
Merciless: Synergizes well with Blood Hunt giving you an extra 5% damage to targets under 40% HP
Dangerous Game: For the 5% HP and Mana restoration when you receive a Kill or Assist on an Enemy Champion.

I usually Start Red or Blue depending on the side I start on.
I full clear my Bot Side Jungle then go to the next buff then Full Clear my Topside Jungle.
If you full clear and kill one Scuttle you can get 1K Gold to get your Tiamat first back because you started Rejuvenation Bead which lowers the Tiamat cost to 1050G.

My personal favorite clear is start Bot Side do Red or Blue based on the side you're on then do Wolfs then your other buff and then invade their Top Side jungles buff and 3 buffing them. Sometimes this can invade will end up with you fighting their jungler at their second buff which unless you make a mistake you should win against most champs in this 1v1 just be wary of the enemy laners roaming to kill you from Top or Mid to punish you for the invade.

Your build path should look like this
Tiamat > Bami's Cinder > Boots > Red Smite > Cinderhulk > Defensive Boots > Titanic Hydra > Deadman's Plate > Spirit Visage > Last Item

Tiamat: Because it gives you AOE wave clear which Warwick very so lacks as he is all single target (Aside from his aoe Fear that does no damage) the Tiamat is nice because once the Jungle Camp is below 50% HP you gain attack speed making you auto more proc'ing Tiamat more making nearby jungle camps get close if not under 50% HP themselves allowing you to use your Blood Hunt Passive Attack Speed on the camp even faster which starts the whole process again.

Bami's Cinder/Cinderhulk: Gives more AOE Clear for the jungle which speeds up your clear a lot and also gives you more Health feels great with your Sustain in fights allowing you to be a Frontline without getting one shot and allowing to use the Sustain in your kit.

Skirmisher's Saber/Red Smite: Gives you more Skirmishing potential as the items name suggests giving you a On-Hit True Damage burn on autos that your Q and Ult applies as well and revealing the targets position for 3 seconds. (Side Note: This does not reveal invisible targets like Shaco, Akali, Talon ETC)

Defensive Boots: use your own judgement on what to build.
Do they have a lot of CC that aren't Knockups/Displacements Build Mercury Treads.
Do they have a lot of AD Champs that auto a lot like Cait, Yasuo, ETC. Build Ninja Tabis.


Finish Titanic Hydra: It adds a small on Hit damage that applies to your Q and Ult. But the active also applies to making your ult/Q deal a HUGE amount of burst and healing you for 70% of the damage it deals on your Q and 100% of the damage it does on your Ult.

Deadman's Plate: Gives Armor and Health but the Unique Passive feels really good giving your more MS to synergize with your Ult making you Dash farther and dealing a small amount of on hit Damage that slows the Target.

Spirit Visage: Gives HP MR and 10% CDR all of which benefit Warwick but the Unique Passive that increases your Healing Done by 25% which Synergizes with your Q and Ult.

Of course get Spirit Visage before Deadman's Plate if they have a lot of AP Damage you want to mitigate.


Last Item:
Guardians Angel: gives Armor and Magic Resist which can be better then Frozen Heart in some games it also allows you to make suicide plays with a second life.
Frozen Heart: I prefer this in most games if I can get away with building it the 40% CDR feels really nice because you can use Q and Ult more for Sustain and it has a built in Attack Speed Slow which is Anti ADC which is nice when you go out of your way to ult the ADC in teamfights. (Side Note: Synergizes well with Ninja Tabis to counter champs like Yasuo, Master Yi, Xin Zhao, and any ADC ETC)

Start Q > W > E
Max R > Q > W > E

Start Q because if you let the Buff hit you twice and then Q you'll be back to Full Hp again. Level W second for the extra 50% Attack Speed on Jungle Camps below 50% HP for Faster Clear. Level E last not because you necessarily need AOE Fear for clear but because the Damage Reduction is nice on the Crimson Raptor Camp and it you get invaded its needed to fight Early.

Max Q cause it gives a nice amount of Damage and Sustain with the extra % Damage up to a total of 10% of the targets health in Magic Damage and healing for 70% of the Damage it deals. (Side Note: On-Hits like Titanic Hydras Active and Triforce apply to your Q which makes it deal more damage and heals for 70% of that active as well)

Max W Second because it gives up to a total of 110% Bonus Attack Speed and 55% More MS on targets that are Blood Hunted which is applied by using W or if they are under 50% HP (Effects are tripled if the target is below 20% Health up to a total of 330% Attack Speed 165% MS)

Max E Last because you only really need it for the AOE CC and the Damage Reduction is only applied to you if you don't recast it for the CC.

Max R Levels 6, 12, 16.

Flash: Personal Preference
Ghost: Personal Preference
Smite: You're a Jungler.
Teleport: Only take if you are going top instead of jungle.

Ghost is an alright pick instead of Flash because it gives you more MS which synergizes with your ult that gets more range based on MS.

Holding down Q on a target makes Warwick jump behind the target and makes you immune to knock ups. (You follow all movement even Flash, Ezreal's Arcane Shift, ETC) You can use this mechanic to immune knockups against champs like Yasuo, Riven, ETC. It can throw people off that you didn't get cc'ed when they used their knockup baiting them and allowing you to when the fight.

You can also use the mechanic explained above to ignore the Dragon's Knock up when you aggro it and it gets up pushing all players/minions back.

Your Ult makes you immune to ALL CC while you are jumped you can do the same thing with your Q effectively if timed right but with CC. (Example you are chasing a Yasuo with tornado but you're not in range to use your Q, when he turns around to knock you up you can ult to immune the CC then suppress him for the kill.)

Save your Q if you know they are about to use Flash after your Ult or just go over a wall with a Flash like ability. It's really enjoyable to follow a Lee Sin's Ward Hop over a wall with your Q.