If I was a Health Care CEO after Luigi and felt in fear of my life from someone else how would I hire security? What would be a good deal? And does security act like the Secret Service to take a bulle

The best security for a healthcare exec is making sure claims get approved at your company. All of them.

The best solution to solving those uneasies would be to make your business less evil and exploitive. The fastest has already been covered.

I can't help but wonder if OP is the CEO of Kaiser Permanente or something... 🤔
- “Let’s just say, for argument’s sake, that I may do things for money that are bad enough that other people want to kill me… how much money would I need to pay someone to not feel that way?”
  
  If they gave me ten million USD (or assets of equivalent value) no strings attached I would stop feeling murderous when I think about that particular exec or company.

So, for the actual answer to how you get private security: you hire a company like constellis (formerly blackwater, or Iraq war crime fame) or the honest to God pinkertons, who are actually still around.
You pay them unholy amounts of money and get some burly people to follow you around, with skills proportional to how much you're paying them. If it gets to the six figure a month range, they also get more war-crime-y because you're going for the highly qualified special forces folks who miss the fun of combat and murder.
If you try to pay what feels like a reasonable sum for private security you're getting a cop working a second job who is definitely not taking a bullet for you, and probably not doing anything more to keep you alive than what's coincidental to keeping themselves alive.
The company I work for does business in countries where kidnapping foreign business people is a common and lucrative way to make money (it's effectively IT consulting, we're not evil beyond the baseline capitalist level). We hire security people for preposterous sums and basically get former special forces who drive a car, make sure the person who showed up to the meeting is actually who they should be, orders delivery food, and tells you not to do stupid things. They try to keep you from getting kidnapped in boring ways, and if you do get kidnapped they coordinate the ransom exchange. (That I know of the most that's ever happened was someone made the phone call to verify that the car they were about to get into at the airport was the pickup, and were told that it was not, abandon your bag if they've already loaded it and immediately go back into the airport and wait for the guard who showed up a minute later and handled the police interaction)
In general just try to avoid being in a position where you feel like you need to have hired a hero.
- Also many of the "private security" (mercenary) companies do union-busting.

Maybe just be a better person and forget the extra security?
- But the shareholders are looking for someone ruthless. Being nice is much less profitable than being an asshole.

You would contact long of the private security firms. Probably something like Northbridge.
Basically, those companies hire ex military and ex LEO, get them reoriented for security qork and farm them out.
A good deal? Depends too much on the threat profile, how big a team you need, how many areas they'll need to cover, how much you travel, etc. But expect to be paying out the nose.
Back when I did super low end security, as in being an obvious bodyguard to deter idiots, my rate was per event, as in you'd pay me to stand there at a party and make sure you weren't fucked with, then I left at the end of an agreed on span of time. A grand would be the norm for me back then.
Someone doing something under contract for someone like a singer, and doing essentially the same thing, you might bring in 50-60k a year, depending on where you are. Higher than that for high profile clients, or with a lot of travel involved. That pricing is pretty old though, so don't try and go negotiating a contract with that info.
Someone that's doing real security work? One person might have a base salary in the 100k range, depending. Someone with some serious credentials like having a background in government security, special forces and the like can go higher.
Generally, if your security detail is taking a bullet, they fucked up. They will, at least in theory. Individuals may or may not actually do so, but they hire people partially based on their willingness to take decisive action like taking a hit.
The few times I was in contact with people like that, they tended to be batshit fucking crazy enough to take a bullet for some rich asshole.
A CEO like that dickweed? Probably has a half dozen people in rotation at most, no ability to control everything, and may or may not be able to afford the hard core people that are out there in that field. That's going to run a fucking big expense per year. Not something they'd be paying out of pocket, even with the kind of salaries they get. If they want the kind of team that can handle even the unrealistic threats, you're looking at a million dollar contract, easy. That's going to be handled through their company, unless the company has an internal security department.
The goal of a security team at that scale is to predict possible attacks, plan for them, and prevent them.
The attack Mr Mangione is accused of, the CEO didn't have serious security, or the shooter couldn't have gotten that close. The client would have had meat all around him, watching for anyone moving into their defined perimeter. They'd have seen someone moving the way the shooter was, and at least have fouled the shot.
The CEOs out there now have whined and moaned into better security. Folks that have kept an eye on such things aren't seeing major activity from any of the big names in private security though. Frankly, they don't need top end protection.

Or just stop murdering people en masse..?

Private contractor. Anyone cheaping out on their own security service isn't likely to survive an actual threat. Depends on who you hire and how much you paying them.
- There are a lot of executive security firms. If you have the wallet They have emergency doctors on retainer, private hospitals, helicopters on standby. Yes they will take a bullet for you, but you'll pay for that privilege. I knew someone who worked for one of the firms in a managerial role.
  
  Trauma Team IRL
  
  But who protects the CEOs of those firms?
- Business must be booming

Private personal security firms exist, and are often used by celebrities, CEOs, and the like. Generally speaking, what you get with those services is just an armed dude who will follow you around and make sure that people keep a safe distance from you. He'll get between you and anybody who may be approaching too aggressively, and will mostly just serve as a physical barrier, more than anything.
They will not take a bullet for you, though. While there's an inherent risk of being attacked as part of the job, they're not going to "get down Mr President" you. While they will do what they can to protect you, they're not going to intentionally sacrifice themselves for you.

Hopefully you would simply choose to change the policies to make it where you weren't somebody that the general public wished were dead.
Otherwise... Try craigslist? I don't know. If you're not willing to try to change the system for the better it's probably better off without you anyway.
- Otherwise… Try craigslist?
  Yes. PLEASE hire your bodyguards through craigslist. I'm not even a CEO killer, but I feel we could ALL use the laughs from how hilariously trashy that would turn out.