TL;DR: You want an AR with a red dot, or holographic sight. And something autoloading in 9mm, ideally with some sort of optic. The Pistol is more relevant.
Now I have a lot to say. We're gonna start with why I made my choices. I have a rifle in 22, in 556, a shotgun in 12ga, and a pistol in 9mm.
I went with an AR, in 556, because that's the default rifle in the US. If you're joining a club, you should have the standard equipment for that club. It's the most common, and the most common chambering. 223 or 556 can be found anywhere. Being common, the ammunition is cheap-ish. It's also quite light as rifles go, fitting your requirements well. An AR in 556 can be had from $450-4000, with most in the $550-1200 range. Mine is made of trash, and litterally hasn't failed in a way that wasn't directly operator error. We'll come back to why this is a good choice for you, at the end. I'm about $900 in on mine, including everything I've bought and then passed on.
I have a AR clone, in 22lr. This is so I can practice for $0.07 per shot, instead of $0.57 per shot. The manual of arms (Read: how you operate it) is the same. The furniture is the same. (Furniture is stock, grip, foregrip, accessories..) so I can train with it, and still instill the same.. behaviors. I have a Hamerli Tac R1. It was $400 I think, and I have another $100 of "stuff' on it.
Both guns have a LPVO (Low Power Variable Optic) which is a adjustable scope designed for "useful" combat ranges. I'm not entirely sure that's the right decision yet, but it's much better than the $20 red dots I had on them. LPVO's give you the opportunity to zoom in on things that are "out there" so you can make better decisions. Ideally, saving you from having to DO anything. I think that's a really important point. Almost as important as.. the next.
You wrote you're looking for a rifle, rifles require.. a plan. You're not going to be "somewhere" and decide you need your rifle and have it. You need to plan for it. Pistols however... you can just kinda throw in the bag, in the car, on your person. While a rifle is a good thing to have, you're more likely to get (as grizzly as it sounds) actual use out of a pistol.
I went with a Canik TP9 because... well. about 70% the dude on the other side of the sales table said he liked it. He wasn't wrong. It's more or less a Walther p99 clone, and while not as nice.. still quite good. Better than I am at least. 18 rounds available, full size, trigger based safety with a nice trigger feel. It came with two magazines and a holster. It's a bit heavy, but heavy isn't bad for a pistol as it reduces the felt recoil. It's good. I'll list what I've shot and my opinions later, so you can judge me silently later. :-) It was about $600, IIRC.
I also bought a Taurus G3c. I went in expecting trash, and walked out the door for less than $270. I can't reasonably carry the Canik, without it being clear I'm carrying, the Taurus is concealable. It's a lot lighter, but recoil hits a lot harder. It is however, Nero compatible, and I'm quite accurate with it. The shorter length does make the sight radius shorter which doesn't help things. It holds 12 rounds.
My opinions are based on the moderately wide range of pistols I have shot. 50AE, 45, 9mm, 270 Winchester (yes, really..), 22lr, and 380. There's been two revolvers, and I don't recall their chambering.
Ok, specific recommendations:
Pistols: What you're looking for in specific is a double stack, striker fired pistol. Chambered in 9mm. People have said Glock 19, they're right. It's like buying IBM, nobody can say you made a bad decision. If you're budget minded, also look at the PSA Dagger. It's a Glock 19 gen 3 clone that seems utterly unproblematic. It's been on the market long enough that we'd know if it had issues. My personal choice of Canik is also good. Don't get something with a hammer.
Rifles: Oh boy, everyone and their brother makes an AR. Get it in 556/223. Palmetto State Armory, Smith and Wesson, Springfield Armory, litterally a dozen other major manufacturers. As long as it takes mil spec hardware, you should be fine. Being a military specification, tons of people have made them. You want a flat top version, so you can mount your choice of optic. Buy a few magazines.
Finally, you have "a" gun. Go to the range, and rent a few guns. A bunch of guns. Some shops have done a $20 or 30 fee, and I could just trade through what they had in the rentals. Other places it's $20 per gun. Either way, it's good to try everything out you can. Learn what you like. If a glock feels like holding on to a 2x4, move on. If a Taurus G3c bites the web on your thumb, find something else. If your hands can't do a double stack, the Glock 43 and other subcompacts exist.
Welcome to the resistance.
I hope you have some sort of therapist to talk to, because this is.. gonna take some work.
Forget the "why". Being there and saving the life of people directly connected to you is traumatic. Full stop. PTSD? I mean, maybe not, but trauma? yes.
There's a lot going on here, and the only reasonable response is advice. You need advisement. You also need to settle the "why". Why the rest of the family isn't concerned? If it's "normal" there's a normalization aspect that needs investigation. Why you have had to do the Heimlich on multiple family members? That speaks to it being something specific about ~your~ family. Why is it YOU who's doing it?
Exactly none of this is normal. Yes, you are having the natural reaction to having family almost dying in front of you. You need to figure out the rest. The other symptoms will either make sense, or go away, if you settle the rest.