I just finished porting an application from Windows into Linux.
I have to create an installer of the application.
The application is not open source
Today, I would also look at Snapcraft and Flatpak which are embraced by some popular distributions. I explored other options and it is what ended up working best for me. Flatpak in particular also helped me learn about standard Linux desktop conventions to follow.
Having been through this a couple of times with commercial products, I think the very best answer is to use the native installer for each supported platform. Anything else produces an unpleasant experience for the end-user, and in practice you have to test on every platform you want to support anyway, so it's not really a significant burden to maintain packages for each. The idea that you can create a binary that can "just work" on every platform out there, including some you've never even heard of, just really doesn't work all that well.
My recommendation is that you pick a platform or two to support initially (Red Hat and Ubuntu would be my suggestions) and then let user demand drive the creation of additional installation packages. Perhaps make it known that you're willing to support additional platforms, for a modest fee that covers your time and effort in packaging and testing on that platform. If a platform proves to be very different, you may need to charge more for ongoing support.
Oh, and I cannot overemphasize the value of virtual machines for scenarios like this. You need to build VMs for each platform you support, and perhaps multiple VMs per platform to make it easy to test different configurations.
I've also looked into this at work and I'd have to agree there really isn't a "best way". If your application is being distributed as source then I'd go with the make/configure methods packaged up in a tar.gz. That seems fairly universal in the Linux world.
A good way to get an idea of what to do is to look at larger organziation and see how they distribute their binaries.
It's possible to install an RPM on Debian and an APT on RHEL.
If you are going to statically link this program, or dynamically link only with libraries that you will be distributing in the package, then it doesn't much matter how you distribute it. The simplest way is tar.gz and that would work.
OTOH if it is dynamically linked with system libraries, and particularly if it has dependencies on dynamic libraries that will be shared with the client's other applications, then you kind of need to do either RPM, APT, or both.
I tell you an additional possibility, although I am not aware of its status: the Loki installer. Loki was a company doing videogames porting for Linux. It went down in 2002, but the installer is available.
InstallShield is also available for linux. No idea on the status though.
Although many people are proposing you to go with tar.gz, please don't. I assume you want to provide a pleasant experience for the installation procedure to your users. A tar.gz is one of the most low level, low quality, low usability choices you can do. It works everywhere because it does basically nothing, as you know.
The guys at freedesktop.org and the LSB are quite clear on where to put stuff. What you need is a friendly program to do that. Autopackage imho has the numbers (I love it), but despite its age, I haven't seen a single program out there distributed as an autopackage.
Evaluate it carefully, but don't skip the chance of being part of the momentum in favour of it, just because it's not popular. If it works for you, and it works for your users, everything else does not matter.
You may also want to look at AppImage (https://appimage.org/). The concept is that it produces a single binary file that the user downloads, sets executable, and runs directly; no installation necessary, no dependencies to install (since the app image typically includes all the dependencies except basic stuff like glibc). This makes for a really great user experience!
Some downsides: