An old fashioned solution such as wood (or faux wood) blinds might indeed be the best solution. I've always liked them for the flexibility they give you in controlling your sun exposure. You can turn them up or down, leave them open or closed, and that gives you all the control you might need. Indeed an old fashioned solution but available now with forward looking appeal in a variety of colors and textures.

I would use one roman shade, maybe a natural woven one for texture, which will look nicer when opened than heavy blinds.