I have like 20 dress shirts and about 15 pocket squares (sales job = leeway for stylish suits everyday)
If you are going to wear a navy suit w white shirt I'd be wearing a white ps. Folded traditionally with just about 1/4" showing from the pocket.
Imo matching the ps to the shirt is better than matching to the tie... Now of course the tie should match the shirt as well. But the ps with the shirt makes it pop.
Couple examples of some of my combos:
Gray/charcoal suit, light blue shirt, gray tie with blue accents, ps not pictured but was blue with white very small plaid
Charcoal suit, shirt is actually mostly white with subtle gray and purple square pattern, tie is purple with slight blue accent and ps is purple and white checkered
Here is a navy one (prob one of my favorite looks), light blue shirt w/a little texture, blue /red tie with red pocket square