A reciprocating saw will be slow to cut logs to length or to notch logs. If possible, I would cut as many logs as possible to length with a chainsaw prior to hauling them to your campground. A decent one-man pulp saw or two-man crosscut saw would be a good bit quicker at cutting logs to length than a reciprocating saw, if possibly more physical labor. My experience with reciprocating saws and logs or pruning limbs is that any larger than around maybe two inches and the reciprocating saw bogs down very quickly, perhaps because the stroke is not long enough to clear the sawdust out of the middle of the cut.
You'll have to flatten and level and even up the tops of your joists to attach decking to them. That will take a good bit of work (and a little bit of skill) with a flat adz or a broad axe if done using traditional mehtods. A portable chain sawmill (or just a chainsaw with a guide of some sort) or perhaps a portable bandsaw would be faster. Ripping a slab off with a reciprocating saw does not sound to me like a viable approach.
For walls, I would probably use saddle joints and "chinkless" construction wherein the bottom of each log is hollowed out to conform to the shape of the top of the log under it. While labor-intensive, those are probably among the simplest ways to fit logs together and they make for a sturdy construction. A curved (gutter) adz is typically used to do the hollows along the bottom of the log, and either axe and adz work or saw kerfs and chiseling with a very large chisel are used for the saddle notches. There needs to be some means of getting logs up to the wall height, such as a ramp or a block and tackle.
Building the deck is a sizable project. Building a lean-to with walls over it is a very large project. It might be helpful to construct a model whittling etc. on some sticks to get a feel for how the joints work and how you need to form the structure and to understand how much shaping is required.
If you're buying new,
Traditional Woodworker is one place to get some of these less common log building tools. They do not come particularly inexpensively. It may well be worth one's while to look for and buy some old or antique tools instead of getting new ones.
