All components of R come in packages (compressed files with code and data inside) that are stored in one of two places on a computer: (1) a user's personal library OR (2) in a system-wide library available to all users. You'll be placing packages in your personal library as you don't have administrative credentials on the Mac Mini.
When R is installed it comes with 'base' packages for working with files, simple graphing, statistics, and working with the operating system (likely macOS in your case). When you start a new session (aka "instance") these 'base' packages are loaded