I think you should go the barkcloth route. It's a nice, heavy-duty texture and there's a huge selection of patterns to choose from these days... all with a mid-century sensibility. I'd go with a reproduction vs. vintage fabric for durability.

Google it for sources. Hey, nice chair btw.

caning is a great eco friendly option and will make the chair look classy too

I have this chair. Years ago, my mother reupholstered it for my first apartment. As I recall, it was fairly easy to do. We used a thicker fabric--probably about as thick as bark cloth--in a solid fabric. It looked great then; it looks great today. I've had it in many different rooms since then. I love it. My advice would be to pick a color that accents your room, just like you'd do with a throw pillow.