Welcome aboard MJVial
Linux Mint is based on Ubuntu and Debian, using the APT package manager. The Debian Administrator's Handbook is available for online reading, downloading, or purchase as book: http://debian-handbook.info/
. It covers most of what you want to know in chapters 5 and 6.
You could also take a look at the Pacman Rosetta: https://wiki.archlinux.org/index.php/Pacman_Rosetta
. Though it is for Arch Linux' package manager (pacman), it compares the package management tools for all major Linux distros including Red Hat/Fedora that you used previously and Ubuntu/Debian on which Linux Mint is based. Might be handy
Another command line tools are mostly the same tools.