I'm a lefty, but use either hand as support for my Sony 505. As it has page turn buttons on both the left and right sides, it makes no difference to me which hand is supporting the reader. That hand's finger can always reach the button.
I still use the original leather cover that came with my reader. I always fold it back rather than keeping it open like a paper book. It's light enough and compact enough to hold with just one hand.
Stitchawl