Smite - Chilling, makes it easier to catch up to people when you run them down
Ghost - Helps for ganks, Lets you just walk through the minion wave and and immense move speed boost

You would start off by getting a Hunters Machete and Rejuve bead
Rush for Tiamat to increase clear

Guinsoo's RageBlade - At 6 stacks You will get DOT every 2nd and 3rd AA, Meaning Full blender mode
Berserkers Greaves - Helps to get your AS up, If you feel like your being CCd alot swap them to Mercury Treads
Chilling Warrior - Extra dmg and also have the smite to slow enemies
Trinity Force - Helps you to stick to targets easier and boost some stats
Ravenous Hydra - Gives some Damage regen and Lifesteal, Helps Wave clear aswell

Phantom Dancer - Gives some AS/Crit and a Free shield
Deaths Dance - Gives more Lifesteal, Good for sustain on long trades
Zz'rot Portal - Gives MS and allows for better split pushing potential

Q - Generally what you want to put the most points into, Every 3rd attack gives DOT dmg which can do immense dmg late game, Your bread and butter
W - Tanky, Good for sustain in the JG or against Dragons or Baron, Every 1st and 3rd hit heal
E - Speed boost and a stun, your initiation ability
R - I never personally use this stance, It gives some wave clear

Conqueror - Your Q will get INSTANT stacks due to the DOT counting as 3 auto attacks, It gives some good damage and increases your lifesteal on W

Triumph - Generally to help save you incase you get low after a kill, and extra gold

Alacrity - Free attack speed, You can get stacks from epic monsters

Coup De Grace - Helps to finish lower healthed enemies

Celerity - Gives your Ghost/E a speed boost to help run people down

Water Walking - Helps to make ganks from river easier

Anything that can lock him down or slow him, If its a melee champ they might have a struggle to fight you after being stunned. My only big issue is Malzahar, due to his free banshees and possibly Riven due to the easy rush and stun

Udyr in my opinion excels in 1v1, but anything that helps him lock a target down works. He works abit better split pushing in my opinion aswell.

I tend to start at my red side, Starting with Q
Get E and rush to blue side, Either get Blue or skip to Scuttle
Finish blue side and then move over to red side, Rush for Tiamat

Infernals are your friend, Aswell as Mountains to help split push
Clouds to help run people down
Oceans Help your laners on the downtime in lanes