I would choose a paint color that plays down the peach and would not use a gray

Find an area that you can "experiment" on with furniture stain and how it soaks into the stone (limestone is very porous). When you find the color(s) you like do the fronts of the stones only and I would suggest lightly sponging. I'm not sure about which finishes are best with heat from the fireplace, I did hear Diamond Hard (like a poly) can take a beating and must take some heat because people use that as the finishing layer when resurfacing their kitchen counter tops. Also, would use the lowest to no glare as possible to keep the look of the stone. I'm not sure if using no sealant is ok with stain on stone. If it is then I would no use any. There is my suggestion. I'm the queen of refinishing houses, in the process of doing another one. Best of luck and I hope what ever you find and do you are absolutely in love with the final result!

Also play with colors for the grout. That could really make the stones pop.

Try a chalk paint (Annie Sloan Paris Grey diluted with water) wash or muted sponge effect on the stone. Chalk paint is very forgiving while you are working it. Not enough color? Add more. Too much coverage? Scrub off with water. I have a big lannon stone fireplace wall and did not like the greyish cement grout and used Annie Sloan to paint the grout. (I tend more towards the old greige than the newer grey colors.) Will you do anything with the raised cement hearth? Just asking as I have one like that and would like to do something other than the whitewash.