The short version: Purple, green and gold, and the more costume the better. Especially on Fat Tuesday itself.
The dominant aesthetics at Mardi Gras New Orleans are carnival costume, full costume, parade and party. That is the visual language of the site, the stages, the merch, the crowd photos, and outfits that speak it look intentional rather than borrowed.
This is a costume festival, and that changes the maths: turning up in normal clothes is the conspicuous choice. Budget for one full look rather than three half-hearted ones, and make sure you can walk, dance and queue in it for eight hours.
What people actually wear: one good layer over a light base, because the temperature halves after sunset; something identifiable, a colour, a hat, a flag, so your group can find you in a crowd of that size.