The Band of the Red Hand started as a group of Tierien & Chairhien (sp? for both) troops that Mat saw was about to wander into a Shaido Aiel ambush. His legacy training & not letting men die attitude kicked in and saved him/them. From there the legend of Mat's battle prowess and luck took over, and people just started joining. You may remember that Mat mentioned that in those times, pay relatively on time & food go a long way....so the band just started to form. Add in the follower's camp which grew up...and there ya go.
Mat's priority was keeping his people safe, keeping them outfitted with weapons, and training. They had battle pennants to keep camp order. When in/around a town, they had a rotation of the "red arms" who were responsible for keeping the peace....
Other then that, I don't remember any type of uniform. It was always described as a mix of this & that from the individual's homeland, or what they had at hand. But you may remember that Tuon remarked that the men were clean & well disciplined. They weren't brigands or thugs (like The Prophet's army). They just weren't a national army. The only non-national armies that had described uniforms were the Whitecloaks & the Dragon's Army.
~Jeordam
Saving the Princess, Humanity, or the World-Entire since 1985