I recently discovered a new type of paper...terraskin. Sounds like a medical procedure for plastic surgery, but no, it's paper made from stone. Yes, stone. Not sure how they make it, but terraskin is water-resistant, tear resistant, acid free with no fiber. No trees, water or bleach were used in its production.
You can use oil, acrylic, ink, pretty much any medium you want directly on it.
I made a few small portraits on terraskin last week and it works beautifully. The paper has an odd feeling of weight to it. It feels heavy and dense. I guess just like stone.