How software gets to your machine, stays up to date, and gets removed cleanly. The package manager is one of the things Linux genuinely does better than every other mainstream OS — once you understand how it works.
Tier 1
Every major distro ships its own package manager and maintains its own package repository. These are curated, tested, and security-audited by the distro maintainers. This is where you should install software first.
Choose your distro family
Tier 2
These formats ship a self-contained application bundle with its own runtime dependencies. They work on any distro. The trade-off is size and integration quality — they're a pragmatic solution for software that distros can't or won't package.
Rule of thumb: use the distro package manager first. If the app isn't there, or the version is too old, try Flatpak. AppImage as a last resort or for quick evaluation. Snap only if you're on Ubuntu and have no alternative.
Tier 3
These aren't for everyone starting out — but knowing they exist helps you understand why experienced Linux users sometimes have strongly different setups.