Is there already a chimney in place? The space looks very small, so consider a thin stone veneer and a small, electric fireplace for the look without the need for major construction. See Houzz photos under "electric fireplace" for ideas of style, incorporating storage.

Installing a wood-burning fireplace in a farmhouse is not for DIY, unless you are up on codes, proper insulation, proper fire-proofing, etc. Save yourself a burned-down house and have a pro do the install. You can save some money with the cosmetic finish work, if necessary.

A Rumford design is very shallow, has outward-flaring sides, a back that arches forward, a curve on the underside of the front lintel leading back to a broad slot-like flue with a flue chamber above it. The overall front opening is almost square, sometimes slightly taller than wide. Rumford fireplaces are very distinctive looking. You can get some basic information from this wikipedia article here: https://en.wikipedia.org/wiki/Rumford_fireplace and there is plenty of info online, even ready-made reproductions (more or less accurate). Rumford developed his improvements and published them in the late 1790s, just before fireplace heating was displaced by stove heating (a process already well underway when Rumford developed his improvements). Good luck with your whatever you decide to do.

Anita Vitrified tiles by themselves do not particularly allow the walls to breathe, and hence are prone to cracking. That being said they do not collect moss either. If you are however set on using these tiles, I suggest you use them in a mosaic fashion, where smaller tiles or broken pieces are used. This will allow the wall to breathe, though the moss collection might be more due to the greater amount of grating.