Avete!
Madder makes a wide range of colors, but tends into the orangey/muddy shades. A good madder red as used in British uniforms has an orangey cast to it, kind of like tomato soup. It tends to fade out eventually to orange or yellowish-red. Here's me as a British light infantryman, 1777:
http://www.larp.com/legioxx/ltbob.jpg
Madder red can be nicely bright, though it is not a blood-red shade and not the least bit bluish, purplish, or wine-red. I have seen very deep purplish tunics used by some Europeans and described as "brick red", and they aren't a madder color at all. It's possible that browner reds were achieved by dyeing natural brown wool with madder, but I don't know if there's any reason to assume that was done. The reds I've seen in artwork don't give that impression, at least.
Why madder? Partly because it's a cheap and readily available dye, partly because Pliny says that it was the most important red dye (for fabric AND leather, by the way!). You can certainly get reds from other sources, but they are more expensive and generally considered luxury colors, as I understand it.
La Wren's Nest offers madder red clothing, though I don't know if they'll sell just fabric. Don't know where they're getting the fabric either, but the color sample I got from them a few years ago was excellent. 18th century suttlers (merchants) such as James Townsend and G. Gedney Godwin are good bets. Just be sure to check the fiber content, if that is important to you.
Valete,
Matthew/Quintus