I would not paint the stairs or railing. Paint will flake and peel, and painted treads will be slippery.

Stain them the same color as the wood on the screened porch, or seal them with a good oil base exterior wood sealer.

I agree with Lyn...............no paint. Stain them. However, it looks like the color of the stairs works with the porch, so I'd be careful about going down this road.