Now, part of going with a "Little Home" is to save money, and just looking at the handtools needed demonstrates that there will be some expenses involved. Decisions of what kind of materials to use, as well as where to get them is a question that will be answered by you, and the factor of time versus money. When it comes to tools, some will say "that can't be done without machinery." Well, the machine is a relatively new thing. In colonial days, everything was done by hand, and even Pre-WWII most carpentry was done, expertly, with hand tools. A circular saw and generator should be prioritized, but a miter saw, compressor, and nail guns may need to wait. A good cordless drill is invaluable, and should probably be prioritized. A high quality chainsaw is critical to Living wih Nature.
The easiest way to get your materials is to take your truck and trailer down to the local builder supply store and buy them. You can get them in the planed smooth dimensions you want. The dimensions are fairly standard, with only small deviations, but the wood is still fairly green, so bows and crooks are still likely if you let it be exposed to moisture for long before you get it in. By "very long," I mean if it gets rained on over night, you could wind up with a pile of rocking chair rockers. If there's dew on your plywood, it may look like a pie pan when you show up. Using ratchet straps to keep it tight and plastic to keep it dry, and/or staining it can help avoid that. Getting it cut and installed and dried in, will also keep it straight.
Another easy, but less expensive way to get your materials is to buy from a small lumber mill. This will mean buying "rough cut" lumber, which will probably be full dimension, i.e. a 2x4 will be 2" by 4" with a rough texture, instead of 1 1/2" by 3 1/2". You can get a splinter from either, and the "rough texture" is more fuzzy than splintery. If you stain it, it'll act like a sponge and really soak up the liquid from a much greater surface area. You could buy a planer and smooth it down, but that does not make it any stronger. When it comes to trim, a planer can be key, but there's little value in planing the framing materials. Add a plunge router to a planer, and you can take that rough cut lumber from framing materials to fine trim, particularly if you buy hardwoods instead of pine.