For the first sharpening tool for your new gyuto, if you don't already have it, I would recommend a quality honing rod (generally referred to as a "sharpening steel", though that term is not really accurate). The quick, stock recommendation is the 12 inch ceramic Idahone, which is available from CKTG for $30. It's inexpensive and definitely much better than mass-market "sharpening steels". The only step better for a honing rod would be the HandAmerican rod - but availability of the HandAmerican is problematic - it might or might not be in either stock or production. You will need the honing rod now, rather than later.
You will be using the honing rod daily - and with it, you can prolong the "new sharp edge" feel on your knife and thus defer the choice of stones for a few months while you check out stone reviews and ponder your choices.
The material making up a honing rod needs to be harder than the steel on the knives which it is applied to. That is not the case with using mass-market "sharpening steels" with quality Japanese knives, where the steel in quality Japanese knives is hardened to a higher level than the steel in "sharpening steels". The result will be damage to both "sharpening steel" and knife edge. Definitely Not Good!
As for a first stone, I would suggest a stone in the 800 to 1200 grit range. If price is not an issue, then any of the "splash and go" stones (the Chosera, Shapton Pro or Glass or Naniwa Superstone) will do very well. I would prefer any of those rather than the King.
The next stone should be in the 3K to 5K grit range.