WHAT MAKES Kha'Zix STRONG?
Extreme burst damage from target-isolated Taste Their Fear, which have 280+2*bonusAD physical damage and also low mana cost and short CD.

Incredible mobility with evolved Leap, especially when Kha'Zix kill someone to reset its CD.

Nice poking ability with evolved Void Spike, which has AOE damage and slow effect.

Take Taste Their Fear and Leap first, which has killing potential at level 2. They can also help you kill minions and escape from danger.

Maximizing Void Spike has great benefit in lane. After you evolve Void Spike, you will be capable to clear minions quickly and going to assist your teammate then.

Evolve Void Spike first, Leap second.
With evolved Void Spike and Leap, Kha'Zix will become a dangerous killing machine.

Evolved Void Assault gives Kha'Zix more sustainability in fight and opportunities to reset passive, but evolved Taste Their Fear deals even heavier burst damage against isolated target. Judge the situations and make a wise decision.

OTHER STARTING ITEMS
Long Sword and Health Potion can't give you enough sustainability in lane.
Elixir of Fortitude is really expensive now.
Wards and potions are still a great choice to start.

Spirit of the Elder Lizard
Since it doesn't give you that much AD, it will not be recommended compared to Muramana.

Ionian Boots of Lucidity
With The Brutalizer, Sorcery, and this, you will have 29% CDR, which lets you using Void Spike and Taste Their Fear more frequently and thus increases your DPS. You can choose Mercury's Treads or Mobility Boots if you think you don't need so much CDR.

Last Whisper
It's the most efficient armor penetration item. However, The Brutalizer has CDR. Thus I choose to purchase this between The Brutalizer and Black Cleaver. You should judge the situation to decide which one is more prior.

Bloodthirster
This item has the most AD within all items except Sword of the Occult. Your skills have 3.7*bonusAD damage in total, so higher AD will definitely boost your damage.

Black Cleaver
It has AD, CDR, armor reducing, and health, but it's a little expensive for these utilities. You will need lots of AD to boost your damage. I always buy The Brutalizer before Bloodthirster, but upgrade it afterward.

Hexdrinker
An efficient item against burst AP champion like Karthus or Lux. Its passive might save your life. Take this if you are facing such champion and upgrade this when they are fed.

Muramana
This provides lots of AD (about 35~60) and nearly inexhaustible mana in middle and late game, while the tear is a burden in early game. If you are determined to take this, upgrade it quickly because the passive of Manamune can be triggered by basic attack while Tear of the Goddess cannot. That makes you stack it more faster.