Hi Sinan.
I don't have experience with this type of metal but here is my idea.
I think mirror finish will be better because it will give stronger contrast when you put paint after you finish your bulino.
I like a 600 grit myself.
To find your go to grit, do several squares on a sheet of stainless using and MARKING each seperate grit, then test engrave and blacken.
What another likes may not be what works for you.
If you have access to a bead blaster I have also heard of glass beads at pretty low pressure just matting up the surface ever so slightly. I engraved a knife recently knocking most of the bead blasting off with really fine paper but leaving a bit of the texture to make it easy on the eyes. It wasn't bulino but... I liked it. It's not going to be everyone/or anyone's favorite but I liked it and will try it again.