When I play him I evolve q, w, e and rarely r
Reason being is my item choices
I 1st buy shoes and 3 pots
then upgrade shoes and buy a phage
then i get brutalizer
then i get trinity force
then either a bloodthirster or a hextech gunblade
then guardian force
then either a bloodthirster (if not gotten before) or infinity blade
then upgrade brutalizer to ghostblade
Reasoning for these choices you may ask? Especially why i get some AP?
Well, his passive deals bonus magic damage based off your AP
Also, the amount of health recieved and damage dealt from your W attack is based off your AP (remember void spikes uses up unseen threat)
Getting the Hextech gunblade has been very usefull for me, especially when you need an unexpected heal from your W in a fight, (Evolving W will give you crowd control slows and if I am correct it heals you more because 3 explosions = 3 chance to heal you, dont quote me on the its hard to tell)
In general I never upgrade my ult, more times than not W is waaaay better to evolve, Q and E are a must though!
With an upgraded ult more times than not youll get owned by team fight aoe anyways and your ult is not going to save you. Khaz's ult is not very good, you weill have rather upgraded your W and have some AP so it actually does damage (because it deals the slow and magic damage from unseen threat and if close enough heals you too!) I can get some champs (lulu comes to mind) to 1/2 health with 1 evolved W attack if they are a couple levels below me.
A good Khazix needs to have a good farm, Poor farm = dead Khazix
Anyways hope this helps, Once someone told me what I'm telling you, I have been kicking some sweet ass with Khazix, though Khazix is very hard to use in teamfights if your team has no good tank or CC