APT or Advanced Package Tool is the command line package manager for Debian based Linux distributions.It provides set of tools to search, add, upgrade or remove linux packages.Some of the tools that users mix and match to achieve end goal of package management are apt, apt-get and apt-cache.

apt

• Recent addition to package management tools list compared to its peers
• Collection of commands for commonly used package management operations making it one stop solution for common operations
• Designed to improve end user experience while working on package management
• More suitable for interactive use than in scripts

apt-get

• Have more options for package management than apt
• Better suited for automation scripts
• Internally used by many GUI based package management tools

apt-cache

• Displays available information about installed and installable package
• Works on the local cache created by commands such as apt-get update or apt update hence output of apt-cache may be outdated depending on time of the last package update.
• apt-cache works in offline mode as its input is local cache

Which command should I use for package management ?

My personal preference is apt as it has easy to remember options usually sufficient for regular package management operations.apt also combines commands from apt-get and apt-cache making it a One Stop Solution.