Over obsessing over a pocket square is not really part of the Ivy tradition. A white linen PS goes well with everything except a white linen suit. Add a pale blue linen/cotton and a paisley silk print and you should be set for life.
Now if we really want to get into the weeds of this subject, I've heard of 2 theories of PS selection. The operative word is they are just THEORIES.
- Coordinate color and pattern of the PS with those of the shirt. They should not match exactly but rather complement each other.
- Contrast the materials of the tie and PS. e.g. if the tie is shiny silk, the PS should be matte linen or wool; and vice versa
But really, it's your wardrobe and your ensemble. I feel you'd almost have to go out of your way to pick a pocket square that absolutely clashes with the rest and therefore is 100% wrong.