Just clean the stone and extend the shiplap across the wall I would not add any shelves. It's too difficult to scribe in next to the stone

If you really need shelves than apply a wall hung bookshelf like these.

I agree with Beverly regarding cleaning the stone and leaving it as is. I don't see the point of painting a fireplace that already has gray stone just another shade of gray. All it will accomplish is taking away the personality and texture of the stone you have.

I like the white wood for contrast since you've already got gray floors, gray walls, and gray stone.

keep it light, like this:

https://www.houzz.com/photos/california-beach-cottage-beach-style-living-room-los-angeles-phvw-vp~37062877

don't paint the stone.

Does anyone know who sells/makes the shelves Beverly posted (in the 3rd picture)?

Here's one that's similar. https://www.amazon.com/dp/B07MNDMBK2/ref=twister_B07X6762G2?th=1

https://www.amazon.com/Nathan-James-65501-Bookshelf-Bookcase/dp/B07F8LYKFY/ref=asc_df_B07F8LYKFY/?tag=hyprod-20&linkCode=df0&hvadid=282226915157&hvpos=1o2&hvnetw=g&hvrand=14615734710477363859&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9016044&hvtargid=pla-491743698161&psc=1

Nice room w/cozy potential. It's small but if well done, it will be a welcoming space.

Thoroughly clean, even bleach, the stone but don't paint it, please. If there will be a tv in this room, over the fireplace would be the most practical place to put it but do consider any local building codes and the amount of heat to which your tv could be exposed..

Shelving left of the fireplace could impede opening the door as fully as you might want. If that is the look you prefer, you might buy one shelving unit and try it both places before buying a second. Because matching the shelving units might be impractical, you might consider a corner cabinet on the right if you're choosing a painted wall around your fireplace. However,

... since that wall to the right of the fireplace wall could accommodate a two seat sofa facing the door or a very large recliner, putting a floor lamp/table combo unit in that corner might be a better idea.

Instead of any built in or wall attached shelving, consider adding a wall to wall horizontal trim board immediately above the stone with wainscoting below and painted wall above. Your ceiling fan has wood look blades so you could choose that wood finish for your wainscoting.

Don't forget to post after pics.