I just looked it up. Miter saws are lovely, and quite safe; you're right about that. They're also pretty specialized. If I were setting up a proper workshop I'd definitely be looking for one. But it wouldn't work for the branches. I need a hand held saw for that.Someone said that tools could be rented. Another possibility that would be safer than a circular saw would be a mitre saw.@Margret
Re:cat tree
I've used each of the types of saws you've discussed. A jigsaw (saber-saw) cannot cut past the blade depth. The tip is not designed to "plunge" into deeper wood. A jigsaw is very useful to cut curved lines in lumber that is thinner than the cut depth. You can also use a jigsaw to cut an "inside" hole in a piece of flat board (like a window) if you drill a hole first to insert the saw blade.
A circular saw can be dangerous, but you can use it to cut wood that is deeper than the blade. There is a base plate with a cutout for the blade. Keeping the base plate flat on the wood helps to keep the cut straight. If the wood is thicker than the blade depth, you turn the wood and cut from the other side. If the wood is more than 4-5" thick, you would need to cut off the center part with some type of hand saw. If the wood is thicker than the saw cut, you need to ensure the wood does not "bind" or pinch the blade, as this will cause kickback,or could break the blade and result in an extremely dangerous situation
A reciprocating saw has several types and sizes of blades available. We use our recip. saw to cut up branches that fall from our trees frequently. This saw works best if the blade is longer than the thickness of the wood you are cutting. The recip saw can "buck" around in your hands, and takes a bit of practice. We cut branches either by going straight through smaller branches, but we tend to cut larger branches by cutting from several directions. You can flip the wood around,or hold the saw to cut the backside of the branch.
I believe you will want to be cutting flat pieces of wood like plywood along with the salvaged branches. The jigsaw or the circular saw will give nice cuts in plywood or particle board, but a recip saw is harder to control and is less likely to provide clean cuts in flat stock. There are fine-cut blades available, but this saw does jump in your hands, and I think it would be difficult to cut a clean, straight line.
You might want to buy a hand saw to cut your branch, like a hacksaw or rip saw (ask at the hardware store), and get a jigsaw or circular saw to cut the flat stock (shelves and platforms) for your cat tree.
You need to avoid "binding" the blade in any case. At best, the saw motor could overheat, and at worst, the blade could break and become a projectile.
You always want to wear safety glasses and ear plugs while running power tools. Safety glasses are a must for any wood cutting activity
Hope this helps.
However, I could easily see renting a miter saw for the walker tray and the shelves of the cat tree. Thank you for the suggestion.
Margret