interesting post,
It's hard to have proof of what colors is used on clothes,
but, think of quite recent discoveries about colorfull statues of different antic period.
Trade in mediterranean area was very important (trade-roads by boat was faster than by foot!)
and an impressive number of raw materials, metals, food, informations and knowledge was diffused around all countries, so the knowledge of coloring clothes.
it's could be more a matter of fashion (already!) and of course the difficulty to produce some rare colors.
so for example it seem than Roman people like White, Purple, Blue, Red, Scarlet, Yellow, Green, Brown, Black...
(but it could be different between town and countryside!)
of course peasants and poor peoples could have no choice that to use natural colors for their clothes (so different wool colors, different leather, and linen like colors...)
and colors could be not so bright and saturate that today (as the color process to fix the color in the clothes was maybe less effective and durable)
i think that merchants, like today tried to make clothes which pleased to their customers, so they tried to be original and beautiful. (and maybe importing rare material from far east)
the question of what is considered as beautiful in Antiquity, in Athens, Sparte, Rome or Babylon for example, is another interesting question!
and of course, some colors have different meaning in Antiquity and for some belief, religions or just decorum that could be very different from one country to another.
(think the use of white or dark for mourning period, or use of particular color for showing religious affiliation...)
But remember that we talk about Warriors, some want to be visible from far away to impress ennemy, (color or drawing on Shields too) but some (especially Psiloi) maybe not want to be seen, so they tend to use natural colors,
and most of them (as it's a matter of money) just wear simple clothes under armor. (and sometimes nothing at all, so it could be impressive to ennemy too, (body painting!
)
the case of Alexandrer the great is interesting too, companions wore very different colors from those we usually see, but Achaemenid Persians too (bright and colorfull armies!)