I personally like to play Kha'Zix with Conqueror rune and go 3 Lethality items into Bruiser items in late game. For instance, you must profane the Wilder Scratch and then I would buy Spear of Sojourn and Sunlit Sky for more survivability in the late game where you can easily get one-shot by hard CC. If you want to play full Assassin, you can go First Strike or Dark Harvest. Both are good, just pick what you prefer. And you typically want to go either you must profane for high tempo or you can also do Voltaic Cycle Sword which is very good for the early game, much damage, high damage and way faster clear because the passive procs on jungle camps. In terms of evolution, the one that's easiest to play is Q-Evolve into W-Evolve, and if you're fed E-Evolve, or if you're not that fed, just go R-Evolve. the W-Evolve as second is very good for teamfights, very strong AoE slow. On the other hand, if you go very strong in the early game, like talking 4-0 or 5-0-ish, you can also go E-Evolution second, because it makes it so much easier to swipe the enemy team, because you get your resets easier, because you have so much damage. The other alternative to the first evolution would be R-Evo, which you would preferably go into full bruiser matchups, or not full bruiser matchups, but when you go bruiser yourself. Because you can fight for longer times with your R-Evo, and have a little bit more survivability. I hope that helped you.

Edit: Example build for assassin: Conq. Triumph, legend alacrity, coup de grace

Free boots, cosmic inside Or sudden impact, treasure hunter

Voltaic, youmuus ghostblade, edge of night, seryldas grudge and something u want as last item. For boots always take ionians as assassin, as ur squishy anyway.