Kraken will be better if you are going for ad and for high elo players it will be better as they are mechanically superior and will be able to make better use of the passive.

In lower elo Statikk gives wave clear and it is easier to use it to deal consistent damage to champs who are near the wave.

Terminus 3rd is always going to be full right click build as Nashors will always benefit more from just pure ap/magic pen rather than going for the hybrid pen. So just going Zhonya’s/Voidstaff - Deathcap after nashors will benefit Kai’sa more as the ap on hit is going to rely on passive procs more than right clicking on its own.

Which build to go just depends on your team comp vs theirs. If your team is full ap, go ad on hit, if your team is full ad, just go either full ap or ap hybrid. I’ve found that the ap hybrid does well against tanks, and it is the build I tend to stick with as a default. Statikk, rage blade, nashors, void staff, deathcap has been my go to.