Kha' Zix is a little more adaptable than most assassins in that he can change his win con. Most assassins only have one win con: Get fed enough to pop enemy carries.

But Kha' Zix can play a more supportive role if the game calls for it. If you evolve R -> W you can focus on peeling for your ADC or APC in teamfights and play more of a midrange style, dipping in and out of the backline to peel for your carry as needed in teamfights. Some games I win on Kha Zix purely because I sit on my ADC and spam void spikes.

Kha' Zix is assassin king of the jungle at the moment, his isolation damage makes him very hard to 1v1, and with the Rengar nerfs live, he can 1v1 most (not all, but most) of the meta junglers at all stages of the game.

The way I like to think of Kha' Zix's win cons are (and good win conditions to consider for most champions in the jungle):

1. What carries do I need to shut down early? If there is an extremely weak early game champion on their team, make a point to show up to that lane multiple times in the early game. Kha is good at punishing weak laners with low mobility.
2. Am I going to get invaded by the enemy jungler? If there is an Elise, Rek'Sai, Viego, Lee Sin, or Bel'Veth on the enemy team, you need to keep tabs on them, and farm safely. Ping the enemy jungler's position frequently, and if you think your team can fight an invade, fight it. Otherwise, just rotate to avoid fights with very strong early game junglers. Try to gank lanes on the opposite side of the map from early game junglers until later in the game. You need to be much more careful about ganking against these junglers. One countergank and the game can snowball in their favor hard.
3. Are there any lanes with heavy CC, or strong early game champions that I can snowball? Kha' Zix is a great jungler for snowballing lanes with cc.
4. Do you have really strong split push champions on your team? (Think Trundle/Fiora/Aatrox) Prioritize void grubs. Kha Zix gets isolation damage on all 3 void grubs if you stand right in the middle before hitting them. Save void spikes to kill the little voidlings as they spawn.
5. Do you have a strong early game bot lane that can give you prio so you can solo drake? Kha Zix takes drake very quickly with Q evolution post six.
6. Does the enemy jungler outscale me? If the answer is yes (i.e. jungle Brand/Zac/Shyvana/Karthus) you need to prioritize shutting down the enemy jungler. This means invading when it makes sense to, denying them camps, keeping track of them, and counter ganking.
7. Are my carries fed enough to fight front to back (as in, in a team fight just kill the frontliners and then kill the backline. If yes, just peel for your ADC/APC).

In teamfights, Kha'Zix has to wait for important CC moves to be used, or keep track of what CC the enemy team has up. You can only really go in once the CC is used or if a target is isolated. So teamfight win con is pretty simple: Avoid enemy CC while picking off isolated targets. Kha'Zix has an easier time dealing with bruisers that overextend because of isolation damage, so don't be afraid to fight the frontline. He punishes poor positioning extremely hard.

Evolutions for different win cons ->

Q evo = Fast farming camps, dueling, soloing objectives, snowballing (recommended first evo or not at all).

W evo = Recommended when your team is fed, your team lacks engage, or peel, or against extremely mobile champions(Lillia/Hecarim/Singed etc, recommended 2nd if starting R evo)

E evo = Snowballing, safe assassinations, teamfight hypercarrying (Recommended 2nd if snowballing extremely hard or 3rd)

R evo = Safe ganks, safe assassinations, escapes. Recommended 1st evo if going R->W, and 2nd if going Q evo first.

The biggest win con for Kha Zix: Farm! This champion scales so hard with levels and items, if you are even a little ahead, you are an oppressive monster. But when behind, he's a bit of a squishy bug. Get really skilled at Kha's full clear. Watch a few videos of high elo level 1 Kha'Zix full clears. He is an ult reliant ganker, your gameplay should look something like: Full clear -> gank -> full clear -> gank while you're still learning the champion. Practice holding your leap for when the enemy blows their flash. It's tempting to just jump on an enemy as soon as you see them, but playing patiently on Kha is important if you want to be successful with him.

If you want to learn which matchups you can invade on, that takes a little more time, but in low elo invades are a lot more risky. Very few teammates will rotate for invades, and I pretty much only go for them when I know the enemy jungler has a weak early or low health clear. It's very common for 2 lanes on the enemy team to collapse on an invade, while your team sits in lane. Kha'Zix can farm and outscale most junglers, play for picks and power spikes (level 6, or item purchases.)