We will set aside the fact that stone is very heavy for the moment. It is hard to transport if you are in a remote place, and will be unrealistic if your home is mobile...up goes the gas consumption.
Stone always has a natural grain, a crystalline structure which is very weak in most cases. It takes practically no flexing at all to crack stone, even the strongest. Stone will take tons and tons of pressure that is evenly applied with good support, but it does not like to flex at all. That means that it is absolutely unsuitable for a mobile house. The jiggling and swaying in even the most carefully reinforced structure will ruin the stone on countertops, walls and floors in no time flat. In a house on piers, you have a similar problem. Any area that has stone resting on it must be absolutely stable and inflexible. Often, the bridge between piers will sag a bit. This tiny amount of sagging can also crack stone. You must really reinforce any area that has stone resting on it. One way to get stone in an area that will flex is to use tiny tiles cut from stone. The grout between them will suffer, but that can be repaired easily. Some stone is installed without grout, as the pieces are butted together and the gap will slide past its neighbor. Still, large pieces will crack if the support is not perfect.
A house with a full perimeter foundation and good floor supports is usually OK...however, if you can jump up and down and notice any flexing at all in the floors, Do not use stone.
SYNTHETIC STONE AND SIMILAR MATERIALS
Corian is the one we all associate with this species of finish material. It will burn, but can be sanded to remove this and other marks. There are tons of other, more recent additions to this genre. Many will be useful additions to a small home. More likely to resist cracking in a flexing situation, it is a better choice for mobile applications. You must consider the weight however. Take along a piece of plywood and compare the weight to a similar size sample of the solid material and make a careful decision as to the weight in mobile situations. I think that floors are unrealistic because of scuffing, however, many people use limestone and marble on floors, and those are very soft. I depends upon whether you are a patina kind of person. The very first scratch is very alarming. But over time a network of scratches can be attractive. Most of these materials have no grain, a much better choice in a mobile house. Good support is, however, a good idea...JUST IN CASE.
I love good wood. However, much of the wood that is used in inexpensive moldings is not meant to be seen. Paint it!
Many of the small houses on wheels that I see are completely clad in tongue and groove inside. It can be quite beautiful if the wood is a decent quality, and even more beautiful if it is poor quality, with knots and marks. It must be uniformly knotted though, and no cracks or checking. Some of the most beautiful traditional interiors have been done in knotty pine and other similar woods. Yew is absolutely lovely, but difficult to find. Pecky Cypress is pretty and can wear like iron.
One thing I do not like about planking the interior of a mobile, or a less than perfectly stable stationary house, is that is squeaks as it moves. The wood rubbing against its neighbor would be awful to listen to on the road(even if you are not riding in it). Even in a stable house, wind pushing at your walls will produce a high pitched symphony.
My other pet peeve about wood in a house is the color. Do not get me wrong. I love the color of wood, but the browns, reds and ambers will just suck the light out of a space! You have to turn on a million lights in a room to just read a book....But then who reads books these days.
Wood also expands and contracts a lot. This leaves cracks and joints opening and closing all the time. This also produces sounds, and can break fasteners like nails over time.
There are two easy ways to conquer the color issue. One is to paint rough cut wood. This will still show wood texture, but give you a reflective surface.
Second, and to many preferable, try pickling the wood. Do not do this to your African or Brazilian hardwoods, but more common woods are a good subject.
Thin down white primer. Paint it on to the wood, and after a couple of minutes or less, (experiment with scraps and do it all in one day) wipe it off with a rag. This will basically stain the wood slightly, and lighten the color, eliminating much of that amber hue that is so bad for light. Do not use oil based paints inside a house as the fumes can linger virtually forever!
I saw a beautiful application of wood in an interior recently. Squares of birch veneered plywood(or other wood veneers) were applied over a base of plywood that sheathed the walls completely. The squares of wood were cut diagonally to the grain. The grain went from corner to corner. A clear finish was put on the squares, and they were mounted on the wall that had been stained darker. The direction of the grain went in opposite directions in a checkerboard pattern. No color differences, but the different directions made the pattern. Very pretty. There was a one or two inch gap between the squares to form a recess and contrasting line like tile grout.
I like tile, but it does not like to bend! It needs perfect support. In a mobile or less than perfectly supported stationary situation, consider weight first, then consider the fact that even the tiniest flex in a tile can crack it. To battle this problem, use small tiles and repair grout as needed. Larger tiles can be a real problem!
Always use porcelain or other very high fired tiles for places that will get wear. Earthen wear or terra cotta. will scar and scratch, and just when you seal it; it will crack or chip on you. Lovely but impractical. Also, Terra Cotta is thick...and heavy as a result.
Never use pale or white grout. Even if you use a sealer, you will eventually get tired of sealing. You may just forget once. Grout stains...no getting around it.
Start with colored or better yet, dirt colored grout. This will drive some of your color choices.
Also, grout can hold smells and mold and mildew. Damp situations must be sealed all the time, and cleaned often.
Stone and tile, and any other polished surface can be very slippery, especially with snow on it! Also, if you drop some thing on it...IT WILL BREAK.
.Carpet absorbs sound. This is a good attribute for a small space and even in a large echoing space. Walls, floors and ceilings can be good subjects for carpet.
It does hold dirt, and bacteria... can be hard to keep in top condition, especially in a space that gets tons of wear...like a small space. Try carpet tiles. Lift and replace them as needed. Think about dry laying carpet instead of gluing or stretching it in a room.
Buy good...no, great carpet. It cannot be terribly expensive in small pieces or remnants. Commercial grades are best. Short pile that will not mash down. Avoid Berbers, and light colors. My navy blue commercial carpet may not be fashionable, with its tiny sprig pattern, but when I vacuum it, it looks the same as the day I had it installed! My back room has carpet that was installed before we bought the house. It is a plush. It crushes and gets dirty and the tan color looks dirty all the time....not a good choice, especially in a high traffic spot...it has paths in it. Who has room for a vacuum in a tiny house?
Think about good oriental carpets with non skid matts under them. Do not use padding under Orientals or put them over carpet. It will break the weave of the Oriental.
Plywood and panels of bead-board are good for stability but awfully cheap looking. The large unbroken expanse of the finish will keep out more drafts though. They help to keep the diagonals of a wall or other surface from moving in the diagonal. To help the look of plywood, try laying and clamping long straight boards onto the surface, and use them as cutting guides for your skill saw or router to make shallow grooves in decorative patterns. Do not try to do this to mimic planks, though, The grain continues through the area and makes it unbelievable. Try squares or diamonds to give interest to the surface. You can pickle the alternating squares or diamonds, stain them different colors, or alternate matt and glossy finishes. Also check out the pickling technique I described under wood above.
Plaster or gypsum board is not a good idea in mobile houses. It is too fragile, seams pull apart...It is best to forget it. In a stationary house, though, you get broad smooth surfaces, color it any way you like, keep out drafts, just avoid it in damp situations, kitchens and baths, unless you use a water resistant variety.
Large sheets of stainless steel, sometimes quilted and texturized are commonly used in automotive situations, and are a good idea for very Spartan modern looks and in damp spaces. Steel is a little hard to maintain. Ask someone who has Stainless Steel for appliances.
The Stillman barn and Elsie.
My sister harvested a lot of boards from the Stillman barn, across the road from the family home in Maine. She used the weathered gray boards on one wall of her living-room and mounted shelves, here and there, using wrought or cast iron wall brackets. She had trailing plants growing on the shelves...very pretty.
You could easily do the same. If barn boards are not your thing or not available, you can sometimes find rough sawn boards, sometimes random widths. Simply give them s light coarse sand...by hand...and when you have removed all the little splinters, nail them to the wall. Paint the wall behind the cracks to match the wood or paint you plan to use on them.
You can have them ship lapped. A rabbet is cut on the edges of the boards, and they overlap slightly to cover the wall surface below.
If you do not like the cracks, you can put strips of wood over the cracks and nail through to the wall between the boards. Planks will shrink and swell with the weather, so this covers the changing cracks. You can buy Astragal molding to cover the cracks, as well, though this would be expensive.
Using planks on a floor can be great. You may wish to ship lap them as above, or cut grooves in the edges and fit a thin piece of wood inside the grooves to fill the gaps(splines).
One issue is whether to paint, or varnish. Remember that paint scratches and wears off. I rather like this, but it can be alarming when the first scratch appears.
Varnishing planks for the floor forms a hard surface, like candy on a candy apple. This is good for dusting etc., but what do you do when the first woman in stiletto heels shows up and punctures the surface? Invite only extremely light women to the house.
Unfinished planking is nice, but it stains. Not a real problem if you like area rugs.