Chalk paint is a great option if the grout is sealed - if you're looking for a single color. Whitewashing it is also a nice option then doing a dark stain mantle would look nice.

I would highly recommend Not painting the stone. I would overgrout it in a lighter ivory or a light color that is in some if the stone. I would also consider capping the bottom step with a limestone base or similar type to update it. I would also get rid of the mantel. It seems too small for such a large fireplace. I would look for a reclaimed wood beam or thicker mantel to give it more character.

Just some samples. You can even change out the fireplace screen to update it. Good luck!