We had to cut a lot of fucking wood over the last few months and now I know way more about saws than I wanted to.
Here's some things about saws.
Miter Saw
We borrowed two different copies of what seemed to be basically the same item: a DeWalt 12-inch sliding double-bevel miter saw. Basically the most or second-most deluxe one they make; I think it's very expensive. And I'm here to say any money spent on a lesser miter saw is basically wasted. As Robert said, "Buy nice or buy twice" (lol). We tried doing some terribly basic baseboard shit with a 10-inch single-bevel one, and no dice! It was just complete bullshit. Don't fuck around with rinky-dink miter saws.
This is the saw we used the most; it handled all the crosscuts on floorboards, all the baseboard cuts, the long-ass crosscuts for the stair treads, and more. Reliable, fast, reasonably safe if you respect it and don't do anything dumb. I liked this saw.
Coping Saw
These are hand tools with replaceable blades. The cheap-ass option works great, and they're surprisingly useful. A coarse blade can stand in for a jigsaw on a fair number of one-off weird cuts. I coped with this saw just fine.
Jigsaw
We used a borrowed power jigsaw that was old as hell and honestly not very good. We were grateful for it and it helped a lot, but it was such a pain in the ass and I never looked forward to using it. I get the impression that even a good jigsaw involves a lot of "oh god, don't go that direction, what the fuck!!"
Circular Saw
Multiple very handy people have told me circular saws are the most dangerous tool an almost-normal person will probably ever use. There's just, like... a risk that if you hit something with a totally different resistance from what you've been cutting, the saw might buck and try to sever a limb. A miter saw stays under control because of the base and hinge, so it might launch a projectile at you but it won't just go fuckin' apeshit.
Ruth said she preferred to never use the circular saw, for reasons of coordination and wrist strength and discomfort. For my part, I decided to never use it unless there was someone else around in screaming distance. Like, I mean, look, it's not like you go in every time being like "maybe this is the time I die" or anything! (After the first few times, at least!) It's fine!!! It's just that it demands some focus and strength and control and some smart precautions, so, I paid the mandatory attention and respect. It was fine.
I got pretty good at it, I think. A lot of what I was doing was ripping (cutting in the direction of the grain, the opposite of crosscutting) narrow pieces of wood, mostly floorboards, and in that case you can't just clamp the piece you're cutting; you have to get creative with like a bunch of other pieces that can pinch it into place and a straightedge you can clamp down onto the whole mass. It was super squirrelly at first, but I eventually figured out some reliable methods.
There's good circ saws and bad circ saws, and I used one of each. The types of difference I was able to notice included the weight, the way the motor responds to being asked to do shit, and the shape and hardness of the foot (square cast magnesium or aluminum is better than curvy bendy stamped steel; with the latter, you're gonna spend 90% of your time wondering just where the hell the saw blade's gonna end up, and it just feels unreliable). We're thinking of getting one of our own, and had decided we'd just go with the Wirecutter's recommended corded one, but then we borrowed a cordless one and damn, the difference that makes in how you work is Not Small. So, now we're not sure what we'll do. If we're lucky we won't need it for a long time anyway!!!
Pull Saw
I don't even know how to describe this, so here's a picture.

We originally got this to undercut the doorjambs and door frame trim, which was a super annoying task that it handled just fine. Later, it came back for an encore role in cutting off the old stair noses, after I'd circ-sawed 80% of the distance.
This is a pretty useful saw. The blade is very bendy, which makes it a little bit ADD, so you have to pay attention and keep it on track. But it is generally friendly and wants to help. When bumped against something, the blade makes an amazing bwwongongonggggg sound.
Sawzall / Reciprocating Saw
This is probably the "right" tool for cutting through stair noses, but it might not have worked in our situation since we didn't want to bung up the skirting too bad. But it was a moot point anyway because we couldn't get ahold of one in time, so I've still never used one. Anyway, afaict it's like a cross between a jigsaw and a jackhammer, so now you know what that thing is called in case you run into a job where you need That.
Wood Chisels
These aren't saws, they're knives with the cutty part at the wrong end. But they're the shit! I need to learn how to sharpen these; we used our set so much that the edges are kind of shot now. Anyway, definitely get some chisels, they come in handy at the weirdest times.