Empirically, among the general purpose, commodity platforms OpenBSD has one of the best track records. Professionally I've had success placing OpenBSD in roles where Linux boxen were constantly hacked. But IT departments in particular, and application developers generally, dislike OpenBSD or would dislike it if it were forced upon them.
More importantly, while nowhere near as bad as Linux, macOS, or Windows, OpenBSD has at least one published severe local kernel vulnerability every year or two. In many cases those OpenBSD boxen I mentioned survived _despite_ being neglected by IT and not kept up-to-date; I know for a fact some were in a known, locally exploitable state for a not insignificant period of time. That makes me think a big part of their relative security is simply related to OpenBSD not being a common target of rootkits and worms. I have little doubt a sophisticated attacker could root an OpenBSD box from the shell, for example, if he was targeting that box. (My rule of thumb when isolating services is that anything running a web service using a non-trivial framework (PHP, NodeJS, etc) provides at least the equivalent to shell-level access to a targeted attacker. Among other things, that means even if I'm writing a privilege separated, locked-down, formally-verified backend daemon, I assume as a general rule that any data it's trying to protect isn't safe from that front-end web application unless it's running on separate hardware.)
While I don't think that security and convenience are necessarily mutually exclusive, as a practical matter they are largely mutually exclusive. Unless you're prepared to accept the burden and cost of using a specialized OS like seL4--and in particular use it in a way that preserves and leverages the stronger security guarantees--your best bet is simply to use separate servers when you want a significant degree of isolation assurance. Separate hardware is not sufficient (if all your boxes have Intel ME cards, or have firmware pushed from a puppet server, or share an engineer's account whose hacked desktop is logging SSH keys, passwords, and Yubikey PINs), but it's largely necessary. This is true whether you're concerned with targeted or opportunistic attacks, but _especially_ opportunistic attacks, which are by far the most common and, in many respects, an important element to targeted attacks.
Separate hardware is a uniquely simple, high-dividend solution. But the point is to be realistic about the actual robustness of your solutions, to be able to easily identify and mitigate risks, so you can make more informed security decisions. And it all depends on what you're protecting and what sort of investment you're capable of making. Just endeavor to predicate your decisions on accurate and informed assessments. Among other things, that means being honest about and understanding your own lack of knowledge and experience.
Similarly, continuity and long-term maintenance are critical to security, which means you need to be honest about institutional capabilities (or for a private server, what you're prepared to track and upgrade 3 years from now.)
Linux, OpenBSD, co-location, and cloud hosting can all be part of a perfectly robust strategy. And HSMs probably should be, too, which is basically just a way to attach a tiny, isolated, dedicated piece of hardware to a computer. But none of these options alone are likely to be reasonable choices, all things considered, especially in the organizational context.