The first picture on that webpage has clear ligatures, the second has light pink powerchains, and the third has no ligatures (they are Damon braces, which are a kind of self-ligating bracket).
If your wife really doesn't want colors and doesn't want to worry about staining, find an ortho who uses self-ligating brackets. Though it's possible she'll have powerchains at some point even with self-ligating brackets, and powerchains will have to be some sort of color (even if it's silver or clear).
Silver is the color that will most look like no color. Blues and dark colors will make the teeth look whiter.
They do get changed out, but it'll be every 4 to 8 weeks. So it's not like you can have red and green just for the week of Christmas, for example. I have braces right now and my appointments are usually 8 weeks apart. That makes picking a color harder because if you go with something seasonal, you have to want to have it for two months, basically.