On typical low-alloy stainless kitchen knives in unknown 'mystery steel', it seems lower grit is better. I've liked the toothy edges coming off something like 220/320-grit wet/dry sandpaper, and have noticed they respond well coming off the 'Fine' side of a Norton 'Economy' Stone (SiC) as well; this mimics the tooth coming off 220/320 sandpaper. These knives don't seem to hold much 'bite' at finer grits; the fine 'micro-teeth' seem to just crumble away very quickly in use. A polished edge on them serves little, if any, advantage; really noticeable on something like a tomato, as the more polished edge loses it's ability to slice it, in low-quality steels like this.
Knives in better steels, with finer grain and higher purity, respond better to more refined finishes and hold edges quite well. Good examples are VG-10 and Sandvik steels, like the 12C27Mod used by Opinel. I've kept stropping & polishing mine to somewhere beyond 2000+ (mirror/near mirror finish), and they've continued to slice like lasers in spite of it all. This means I can maintain them almost entirely on a strop (hard-backed), without having to periodically go back to a coarser grit stone or sandpaper to restore the 'bite'.
David