There is a color that is more versatile than any other, it would be white. There are just hundreds and hundreds of combinations of things you can do with white baseball caps. They can be turned into flags rather easily or just be worn plain. I would suggest some color due to the fact that they can show dirt rather easily. You can use whatever method you wish to put some kind of design on the hat. If you do not want a design put on the hat, you can go with a name or just some strange pattern. There is no limit as to what you can do.
White baseball caps are very popular with professional team as well. Just about all teams have primary colors. For something that will go with just about anything, white baseball caps can be used. They can have the same logo on a white hat as they do a normal colored hat. Or maybe they come up with a new design or logo altogether. There are so many choices that can be done with this.