There are those who wear their pocket handkerchiefs to pick up a color in their necktie, but I think it looks less studied to complement either the shirt or some part of the pattern of the jacket. Those two criteria tend to favor the color white, which is usually present in one or the other. And since silk neckties should ideally have a drier complement for that same less studied purpose, the white linen handkerchief finds its way into worsted breast pockets more often than any other choice. Shinier silken squares should ideally be reserved for days when they can accompany a knit, grenadine, cashmere or other sheenless necktie.
Linen is better than the cotton alternative for a display handkerchief because it has enough body to remain upright in a pocket all day long (that same body makes it somewhat less effective for the other purpose to which handkerchiefs tend to be put until it has been washed enough to soften considerably, and by that time it is of course less effective for display).
Remaining upright is important, for the linen handkerchief should be worn with its points up. Forget about the tv fold, that refuge of the insecure. Displaying a handkerchief's points implies that it has been stuffed carelessly into the pocket, in keeping with the unstudied look that, to paraphrase the late dandy Douglas Fairbanks Jr., often takes considerable time to actually accomplish.
Points up please.