1. Get a copy of the Amiga 3.1 Kickstart ROM (v40) and Workbench disks (for example by legally buying Amiga Forever ... or other ways). If you do buy Amiga Forever, they've put together an Amiga emulation environment for you with lots of software pre-installed.
2. Consider buying AmiKit or using its free version: https://www.amikit.amiga.sk/ -- it needs the aforementioned Kickstart ROM and Workbench Disks, but again they've put together an Amiga emulation environment for you with lots of software pre-installed.
3. If you don't want to use those pre-made packs, install WinUAE (for Windows) or amiberry (for macOS/Linux) yourself, configure them yourself with the ROM... and use one of the ClassicWB (https://classicwb.abime.net/) hard drive images.
4. And if you don't like ClassicWB, you can also extract the Amiga hard drive image included with PiMiga 4 to enjoy an alternative pack. PiMiga is a Raspberry Pi image that includes an Amiga emulator for the Pi and a huge Amiga hard drive image -- simply use software to read the PiMiga Linux ext2 filesystem and extract that hard drive image to use it on your own emulator, no RPi needed (https://old.reddit.com/r/amiga/comments/1dfcn8u/extract_amig...)
If the aim is to emulate games, Kickstart 3.1 or even 2.04 shouldn't be the first choice. Backwards compatibility must have been really poor back then; at least I've run into lots of software that will only run on 1.3.
One does not typically run games directly. That's fraught with the compatibility concerns you raise, and also the slowness of loading them from their disks, even when using an emulator, and needing a cumbersome UI to swap disks as needed.
Instead you run them with WHDLoad, originally designed to install all games onto the hard drives of real Amigas.
A lovely group of programmers have made WHDLoad installers for every game you know of, that patch the game in just the right places so it runs correctly, regardless of Amiga model or OS version.
WHDLoad also lets you press a "QuitKey" that returns you back to Workbench. And if you have an emulated Amiga with lots of RAM, you get to preload all the disks into RAM so there's basically zero loading time.
People have made large collections of "preinstalled" WHDLoad installers, bundling games in a ready-to-run way for any Amiga.
2. Consider buying AmiKit or using its free version: https://www.amikit.amiga.sk/ -- it needs the aforementioned Kickstart ROM and Workbench Disks, but again they've put together an Amiga emulation environment for you with lots of software pre-installed.
3. If you don't want to use those pre-made packs, install WinUAE (for Windows) or amiberry (for macOS/Linux) yourself, configure them yourself with the ROM... and use one of the ClassicWB (https://classicwb.abime.net/) hard drive images.
4. And if you don't like ClassicWB, you can also extract the Amiga hard drive image included with PiMiga 4 to enjoy an alternative pack. PiMiga is a Raspberry Pi image that includes an Amiga emulator for the Pi and a huge Amiga hard drive image -- simply use software to read the PiMiga Linux ext2 filesystem and extract that hard drive image to use it on your own emulator, no RPi needed (https://old.reddit.com/r/amiga/comments/1dfcn8u/extract_amig...)