If you want to run your own antique IBM mainframe operating system at home the first step is to install the hercules emulator. And then select the O/S of choice from the many available options, some easy to install and some a lot more complicated.

Obtaining the Hercules emulator, so many options

Origional/Offical at http://www.hercules-390.eu

The lastest official version of the Hercules emulator is available at http://www.hercules-390.eu/. This version is the one packaged in most Linux distribution repositories, fairly stable and not much ongoing development.
Quickstart tip: Fedora/CentOS/Redhat users can 'yum install hercules' to obtain the official version, it's in the repositores (as of 16 Nov 2020 at version 3.13). Repository versions (Fedora anyway) do not provide working tcpnje devices so be aware of that; it cannot be used for nje38.

The spinhawk sources on github (my current preference)

The latest hercules 3.xx source appears to be 'spinhawk', it is at https://github.com/rbowler/spinhawk which does support the tcpnje devices. This seems to consistently provide a stable environment and featurewise is a long way ahead of what is bundled in the OS package repositories and the hercules-390 site. This is the version I am currently using.
As always review the known known issues with spinhawk).

The more frequently updated fork, the hyperion sources on github

There is also a fork of hercules named hyperion running a 4.xx release stream; the source for that can be found at https://github.com/SDL-Hercules-390/hyperion which is a stream undergoing a lot of active development. This has diverged from the main hercules stream and is no longer fully compatible with in operatation or utility usage of the 3.x streams. There is a YouTube tutorial on compiling it by moshix at https://www.youtube.com/watch?v=DwBbnjC0Hco if you want to go down that path.
As always review the known known issues with hyperion).

And a modified version for mvs3.8j enhancements

There is also a version of hercules being modified to allow mvs3.8j additional features such as 31 bit addressing

My notes on all this

If you need additional features provided by hyperion use it. If you do not but still wish to play with the latest toys such as nje38 you will need spinhawk which I personally think is more stable (review known issues for both on theit github issues pages and make your own choice). If you just want a rock solid hercules environment with none of the features added in the last 5-6 years just use the much older version packaged in your OS distribution repositories.
The key thing to remember is that the streams have diverged, there are enhancements in hyperion that may never be backported to spinhawk, likewise enhancements in spinhawk that may never make it to hyperion; they will behave differently so just chose the one that meets your needs but do not expect them to behave the same way.

Lots of operating systems to choose from

Reguardless of which version of hercules you chose you still need to install an operating system to run under it for it to be useful to you of course.

I have a list of operating systems available that I am aware of so far that you may be interested in running under hercules. I expect the list will also grow over time.