So, for runes you´ll want to take Electrocute. It´s definitely the best on Neeko since her Blooming Burst can hit 3 times. You usually do your combo with more than 3 hits.

You can choose between Taste of Blood and Sudden Impact. I usually take Taste of Blood because I prefer to heal from abilities and Sudden Impact is great when you use your Shapesplitter. If you don't use this abilitie much, then consider changing to Taste of Blood.

Hunter's Talisman

Between Hunter's Talisman and Hunter's Machete you should pick Hunter's Talisman. It's like having a red buff always while in jungle, healing you with damage dealt from your abilities, making it a viable item.

Health Potion

Most people would take Refillable Potion instead, but since I changed to Health Potion I´ve been much more stable in early game. Buying 3 potions instead of two than heal more over time is a good deal. You won't have to buy potions everytime you go to base, maybe in the first back, but you'll have more sustain and won't need to back as early, giving you advantage over the enemy jungler.

Stalker's Blade

Granting Life Steal vs monsters, Stalker's Blade is a great item that'll make your jungling much easier. It also grants you Chilling Smite so don't forget to use it during team fights.

Boots

Sorcerer's Shoes is the best buy most of the time, giving you magic penetration. However, if you're against a heavy AD champion like Zed or Yasuo, consider taking Ninja Tabi.

Hextech Protobelt-01

I usually rush this item after Stalker's Blade - Runic Echoes because of the dash. In most team fights where the enemy gets away, that little dash would help so much. Granting you 10% cooldown reduction and 60 AP, Hextech Protobelt-01 is a great second item for Neeko in any lane.

Morellonomicon

You don't need to buy this item if you're ahead, but granting 300 HP, Morellonomicon can change your game.

Rabadon's Deathcap

This is a must have in any Neeko build. Granting raw AP and incresing your total AP by 40%, Rabadon's Deathcap is most loved by mage players. From the moment you buy this you'll be a monster and probably focus by everyone in the enemy team. If you hit you Tangle-Barbs no one will be able to stand against you.
Get this third item or second if you're ahead.

Zhonya's Hourglass

Rush this if you're against Yasuo, Zed or any bursty AD champion. Learn how to use it with your ulti in this guide.

Void Staff

Save this item for last. You only need to get this if the enemy is building magic resistence, which won't happen if you're team is made of AD champions.

Start on botside with leash from botlane. Get the wolves/raptor, scuttle and the other buff. You should get level 3 by then.

Best Clear Path

If you want an early lead, start on the wolves and kill the biggest and ONE smaller one. Get the blue buff, scuttle and the smaller wolf. You should get level 3 in about 3 minutes. This is the most efficient way of clearing the jungle in this season.