What is the highest system that you have installed on your mini?
If you have already been using Catalina, then it's pretty simple, and easy to check.
Boot to Internet Recovery (Restart, holding Option-Command-r)
You will see a spinning globe, not the usual Apple icon. You will be booting to Apple's remote servers, which might take several minutes to finish booting.
At the menu screen, choose Reinstall macOS.
The installer will launch, and you will see by the launch window what system version will be installed.
If Catalina appears there, then you might be ready. Quit the installer to return to the main menu.
If you have anything on your drive that you need to back up, do that now. If you have nothing to back up, and you are ready to erase the drive, then open Disk Utility, and erase your drive.
Quit Disk Utility.
Choose Reinstall macOS.
Choose your newly-erased drive for the destination, and begin the Catalina install.
Internet Recovery will download the Catalina install then, continuing with the install. So, the download will depend on the speed of your internet connection. Get a cuppa coffee, this will take some time, but you will then have your fresh install of Catalina.
(If you have NEVER installed or upgraded to Catalina, then you will need the Catalina installer on a bootable drive to get there, but that's just a minor challenge.)