Yeah, if it were me, I would probably use more of a matte fabric, but something significantly nicer than broadcloth. I used to make my early costumes out of broadcloth, not even thinking about different textures and fabrics. -_-'
I wouldn't use a shiny fabric either, only because the costume doesn't seem like it would suit it very much. Not many anime/game outfits look like they are made from something shiny, but maybe that's just because it is more difficult to animate... In the picture I attached, it really doesn't look shiny to me.
It's a little difficult to describe the type of fabric I would get for this without going to a fabric store, taking a picture, and posting it on here.