i use a host of traditional polishing stones for anything i have done involving a hamon. and use various arato, binsui, kaisei, chu-nagura, koma-nagura, hadori, jizuya, uchigumori, and nugui. to name just a few.
for non japanese style blades, i use binsui, lansky stones, arkansas stones, and some generic ones ive picked up over the years. to be honest... they all do the same thing. its just my preference.
i also love pieces of steel ive collected from metal laythe's. i believe their the cutting bits. they make perfect sharpening steels, and can easily be picked up cheaply.... i honestly dont think ive got a favourate method of sharpening. considering that the outcome is the same. it relies on how im feeling, and how close a certain stone, or steel is. i just have a wide selection cus things tend to accumulate.