I experiment a lot, but it really depends on the steel and function of the knife...
On beater Victorinox, etc, I've been sharpening and finishing on a JNS 800 after setting the bevel on a coarse diamond plate, and stropping on bare leather. Surprisingly, the JNS 800 munches through cheap SS, and leaves a decent working edge that can start to shave whilst maintaining an aggressive tooth. Nice feel, too, on steels that typically feel awful to sharpen.
On my Aogami knives, I'm typically finishing on my Belgian Blue, or a Shapton or Gesshin synth in the 3-6K range. Edge leading, then stropped on bare leather. I just always love sharpening this stuff. It wants to get sharp and toothy.
On Shirogami, I typically finish on my Aiiwatani from Maksim, and then strop on bare leather... Getting that 'sharp / toothy' balance, that lasts, is harder on Shirogami than Aogami. So far I find it works best if you use J-Nats, take it a little higher in the grit range than you would Aogami, and strop it routinely between low-volume meal prep. With synths, 3-4K seems to be a sweet spot, but J-Nat is better for sharpness/retention. In this circumstance, it holds its edge quite well, and is easy to sharpen.
For vintage French carbons, I love the finish I get off of my Translucent Arkansas, but it takes some time... I have a La Dressante Coticule that is faster and toothier feeling, but doesn't last quite as long on the edge. Routine bare leather stropping... These knives really make me feel I should get a steel.
Decent culinary stainless is a bit pickier than carbon... I have favorite stones for different knives.
I like my Gesshin 1K/6K Combo or a full J-Nat progression on Hiromoto's Ginsan, Gesshin 2-4K on Suisin AUS-8, La Dressante Coticule or synth from 6-12K + Diamond Strop up to 0.25 micron on SRS-15, JNS Blue Speckled Aoto for SLD, etc.
Folders I tend to take pretty high... BBW, 6-12K Synth, Pasted Strops, etc.
Butchery knives I leave as low as they can go and still deburr and shave... Typically Shapton 500 GS or Naniwa 600 Pro.
- Steampunk