I do not like anything under about 2k-ish as a "working finish" on a knife, depending on the polishing medium.
For natural stones, I think my binsui/aizu/igarashi are OK, but a little coarse with base stone slurry, and a finer nagura on the stone gets it in the right neighborhood for a low-grit working finish.
For synthetic stones...the red synthetic aoto (2-4k mix) from Maksim is OK, and I will use it to "tame" an 800-grit finish, which is way too coarse for me (the fogging masks it but the drag is there).
For diamond pastes on paper or balsa or whatever (not very often) I think 2-5k is generally fine.
For sandpaper, 1200-2000 grit is generally satisfactory, chased with some autosol.
For 3m polishing sponges, Superfine (400 grit) is a good start and microfine (1500ish?) is usually plenty, but these cut very differently from other media.
It's hard to make any absolute statements since I mix media pretty often.
I do not think highly polished surfaces cause significant sticking, though they might exacerbate a problem if the bevel is too flat and thin.