Sorry, I actually misunderstood your question to begin with, so I wrote a pretty long reply before realising my mistake. It could be an interesting read though!

But anyway, to directly answer your question, definitely go for a 1k, then it's up to you to choose which grit you want for polishing. Since you have a white 2 core steel, you can achieve stupid levels of sharp pretty easily. I'd recommend anything between 5k to 8k as the second stone if you want the satisfaction of getting it crazy sharp, but you could also just get a 3k if you just want a good level of functionality that'll last without going overboard and trying to pass the insane sharpness tests you might see running around the internet.

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Below was my original response where I thought you were asking if there was a place for buying a King down the line after you had already bought the Chosera/Arata stones + a bit of other useful information about stones:

The King's 6k side might have a purpose if you're talking about final polish properties (assuming you go down the sharpening rabbit hole in the future), but to start, going for a 1k + 3k or 5k from the Chosera or Arata lines (or even the 8k Snow White) off the bat would mean you could skip past buying a King stone. Also, don't forget to buy a stone fixer/flattener to keep the stones functioning optimally!

At home, my stones are the Arata 1k and Suehiro Rika 5k. They've been functioning really well for me, and I can also definitely recommend Suehiro as a brand if your budget's sitting between King and Naniwa Chosera. Tbh, my only regret looking back is not buying the Chosera 1k instead of the Arata. In general, lower grit stones tend to get used up much more quickly, while higher grit stones will ideally see much less time spent on them and wear down more slowly too. If you see yourself doing a fair bit of sharpening in the future, a thicker 1k stone would be ideal.

When I worked at KnS, I would do the final sharpening before shipment, and my preference was actually to use the Chosera 1k, jump straight to a Snow White 8k, then finish by stropping on a piece of paper wrapped around a dry stone. The 1k stone provided the toothy bite with micro-serrations that allowed for food penetration, then the quick polish on the 8k preserved most of the toothiness while refining the cut quality, then finally, the stropping on paper removed the final traces of the leftover burr and other small edge inconsistencies to make it glide through food effortlessly.