My opinion on the gun stuff
5.56/AR15: Yes. It's ubiquitous, cheap, effective, numerous platforms, very controllable. Basically no reason not to have one if you're going to own multiple weapons. Might not immediately pierce a plate but if you put a couple of rounds into one the plate will crumble and it will penetrate any soft armor
For a pistol, a 9mm glock in your preferred size. 17 or 17L for full size or 19 for something a bit more compact imho
For a pistol with more oomf, a revolver in .357 is always a solid choice. You can run .38 specials in it for performance/recoil comparable to 9mm or jump up to .357 loadings for more power. I like the Ruger GP100. Alternatively, a Glock 20 in 10mm is a ridiculous amount of firepower to have in a handgun
.50BMG: Recoil isn't bad at all, the guns are heavy and they all have brakes, I'd compare it to a 12ga shotgun for a bolt rifle, never shot a semi-auto one but they should have less recoil. My .300win mag is definitely way more brutal on the shoulder. It's gonna be basically useless for self defense. The rifles weigh 20-30 pounds with a ton of that being in the barrel which makes them difficult to fire from the shoulder. You have to be laying down or at a bench to fire them effectively. I have a physical job and work out a lot on top of that, I can shoulder a Serbu BFG50 (a bit over 20 pounds with bipod, scope, etc) while standing but I'd never be able to make a shot at any real range like that, let alone with my heart racing. The lightest .50 you can get is about 2 pounds lighter and costs about 6x as much. If you really want a usable .50 the M82A2 is the only one I've seen that you can kinda run around with, but only 10 were made so whenever one goes up for sale you're going to have to be ready to throw absolute wads of cash at it
.50BMG seems to have mostly been supplanted with .338 Lapua Magnum, about half the energy of a .50 but it's much lighter and also much more accurate, since it was actually designed as a precision round rather than anti-material. I don't have any experience with it so I won't give particular suggestions, but just looking quickly it's $6-8/round so a bit more expensive than .50BMG on average but they're in the same range, but the rifles are cheaper/slightly lighter, and probably better balanced since they don't have to have the .50's barrel.
If you're worried about body armor you probably want a .308/7.62x51 instead. I'd call them the 5.56 of big boy cartridges where it's available, cheap, and easy to find a platform to run it in. Personally I'm a big fan of the M14/M1A but you can also get an AR10 or any number of other rifles. It's basically
the hunting round so you've got a ton of options for bolt action rifles as well.
If you're legitimately in 'price is no object' mode and want to defeat plates I think the HCAR would be my recommendation. 30'06 is the only caliber you can reliably get AP rounds in, if you're willing to buy in bulk you can get them for as little as $1.50 a round, and the HCAR mags hold 30 rounds.
An M1A with the classic wood furniture would honestly be my primary recommendation to you for a self defense rifle, along with one of the glocks I mentioned as a pistol. If you go to court they won't be able to hold up a big scary black assault rifle and try to use it against you, and everyone has a glock so they're not scary either. You get 20 rounds of 308 with the box mags and they're just sexy as hell
For the same logic, a Ruger Mini 14 would be a good alternative to an AR15 for a 5.56 rifle, just looks a lot less scary to normies