Re: Can you suggest milking Genre game?
The only "game" I can think of that centers around milking involves Tifa from Final Fantasy 7. It was memorable for me.
It's called "Milk Plant" or "Milk Plant Battle Girl" and it has multiple chapters. I seem to recall chapter 3 or 4 has some nice mechanics/scenes in it.
It's more like a visual novel, but you can control some things to an extent.