Add color column in categories?

Is there a way to add a column to the categories for color and have default set to sort by color? I’d also have to know where to add color as a sort item.

I’m working on a website selling jewelry beads for my wife and she’d like to have the beads sorted by color by default instead of “Name”, “Price”, “Popularity”, or “Bestselling”.

Can’t put color as the beginning in the name, because take blue, there are many shades of blue.