If you live in a hot climate or are blessed with southern exposure, consider the simplest drapery in the world. Hang plain, unlined swaths of inexpensive linen at the windows. Yes, the linen rumples. (Let it.) Yes, it eventually yellows in the sun, and must be replaced. But it has an easy elegance.
Hang the linen from a dark-stained wooden pole using wooden rings (from any fabric shop) that you sew to the top of the draperies.
Tip: Wash the curtain and let dry in the sun before hemming. Do not iron.