external hard disk format for mac linux and windows

Since you say you are new to Linux, and because the stuff you want to do can go wrong if you make a mistake, I highly suggest making a full backup of your macOS system before anything. It's like pulling your own shoes to lift you up The problem you are encountering is because you are trying to install on the same disk you are booted from. You normally also do not need to format the drive, just use Etcher and it will do the formatting.

A 4GB flash drive is sufficient (maybe even 2GB is enough). You do not need a whole external hard drive to make a live USB. I am not much of a Linux techie so please make your reply easy to follow. I assume that after a correct installation I shall be able to boot the full MintOS by holding the 'Option' key and shall be able to save all changes when I log out of each session. Please correct this from the partitioning menu', then I just quit the installation. I successfully complete all the steps including selecting my 500gb drive as the destination drive, then when I click on 'Install' get a message saying ' No root file system is defined. Now I want to permanently install Mint 19.1 to this same 500gb external hard drive because I want to save the changes I make after each session. This live USB loads perfectly by using the Option Key on my iMac.

I made a live USB of Mint 19.1 using Etcher on a 500gb External Hard Drive with a format of MS-DOS FAT using Disk Utility to format on my mac running Mac OSX Yosemite. I am new to Linux Mint, am very anxious to make it another OS.

External hard disk format for mac linux and windows