The steps are wood. We could use steel diamond-plate

I could paint the steps but I think a natural wood will
look better. So I'm thinking of using varnish or
poly-urethane.

If you use varnish or paint, the step you use will be getting scuffed up.
Maybe a deck stain with some sand sprinkled on for non-skid. Weathered wood
sometimes isn't too slick.