Classic Evelynn Jungle

Smite flash standard.

Hate Spike (Q) is our main damage dealing and main clear ability. We want to max it as soon as possible. It's range allows you to essentially be a ranged champion against bruisers that will beat you in auto attack fights. Combined with Dark Frenzy (W), you can run circles around them and take minimal amounts of damage while constantly dealing damage.

Dark Frenzy (W) is a great mobility skill and slow breaker. Make sure to save it for strong long slows like Wither (W) Ice Blast (E) Mocking Shout (W). We put a second point at lvl 8 since the MS from hitting a champion double from 4 to 8, which is a lot of mobility in fights which will translate to more damage dealt and less damage taken assuming we use that MS properly. Don't be afraid to spam it in between camps if you don't need mana regen from being invisible.

Ravage (E) is a great burst and attack speed steroid. Use it in combination with Hate Spike (Q) to clear the jungle extremely fast. Unfortunately, this ability does not apply on hit effect, so it limits our itemization options, but the burst it has and the attack speed steroid are quite powerful in long fights, but be careful not to greed with too many auto attacks against melee bruiser as your main strength is the damage and range on Hate Spike (Q) letting you deal damage without them being able to hit back. Against ranged champions, it's different, we want to maximize the attack speed steroid to get more auto attacks in.
Agony's Embrace (R) is a great engage ability, AoE CC ability, AoE Burst ability and a great defensive ability. You want to open teamfights with it as it deals current health damage, meaning you will get more value from it as they are full health. Combine it with Deathfire Grasp to burst down a single target then use the massive shield it gives you tank and deal damage with your low cooldown Hate Spike (Q) .

Marks: Attack damage. This will give you the best mix of clear and damage throughout the game. Since you have a AS steroid from Ravage (E) , you want to have some AD to benefit from it. You also have AD ratios on Hate Spike (Q) and Ravage (E) for it to scale.

Seals: Flat armor. Mandatory for clearing the jungle on Evelynn. Other option could be health per level, but you would have to go armor quints which is ok if you plan on going a tanky build.

Glyphs: Scaling AP. Best source of damage and scales very well. If you prefer a more defensive option, go for scaling MR instead. Since there is a lot of AP champions in the roster, I'd advice going scaling MR in most situations.

Quintessences: Flat AP. Great source of damage and scales all your abilities while also helping with clear / early damage. You could also consider Movement speed if you want the extra mobility, but it will affect your early clear a little bit.

21 Offense:
We want to maximize our clear speed, so butcher is a great source of damage against the jungle which is made stronger by grabbing the attack speed and Ravage (E) .
Since she mostly does magic damage and scale off AP, we want to grab the magic penetration as well as the AP / % AP and Spellsword to get the most damage out of the AP items we will buy.

9 defense:

Durability + veteran's scar gives us quite a bit of early health HP and scales well. Since our early clear makes us take a fair amount of damage, getting extra damage reduction from monsters helps a lot, especially if you are a newer player. Finally, the augmented smite is worth roughly 1.25 gold per 10, so it is worth getting in my opinion.

Alternative page: https://imgur.com/a/nRvOagN
9 offense:
We want to maximize our clear speed, so butcher is a great source of damage against the jungle which is made stronger by grabbing the attack speed and Ravage (E) .
Since she mostly does magic damage and scale off AP, we want to grab the magic penetration.
21 defense:
Durability + veteran's scar gives us quite a bit of early health HP and scales well. Since our early clear makes us take a fair amount of damage, getting extra damage reduction from monsters helps a lot, especially if you are a newer player. Tthe augmented smite is worth roughly 1.25 gold per 10, so it is worth getting in my opinion. We then want to get extra tenacity and % hp which will allow us to be a lot less vulnerable to CC and scale our high HP items like Rylai's Crystal Scepter or Randuin's Omen a lot better. The reduced critical strike damage taken is amazing against late game carries, but is also very good against Tryndamere Gangplank Shaco .