I've mostly used cotton lycra or jersey-knit fabric (t-shirt material). It stretches nicely, and the subtle ribbing makes an easy guide for cutting a long, straight edge, if I'm careful.
Style has either been a breechcloth with a belt, or a longer cloth wrapped around and tied in back. I've described both at www.aaronofmpls.com/lc/.
Mostly cotton or linen.