Arch is a rolling relase GNU/Linux distro that does not come witha GUI by default. If you want to use Arch on a server or workstation, you will need to spend more time on maintanance. It is a distro for enthusiasts and is not as solid a solution for production environments. It includes proprietary software in its repos.
Arch uses a package manager called Pacman. Pacman has commands such as "pacman -S" to install software, "pacman -Syu" to update and upgrade the system, and "pacman -Ss" to search the repositories for packages. Packages are divided into several repositories such as core, exta, or community. However, this devision jumbles toether free and proprietary packages, making it more difficult to avoid software with odious terms.
Debian is one of the oldest GNU/Linux distributions. It is very stable and so is a common choice for servers and workstations. It makes for a good, light desktop too. Debian ships proprietary software, but libre and proprietary software live in separate repos.
Fedora is a relatively stable short term release distribution using the rpm and dnf package managers. It is a popular desktop and workstation distro and offers a good server image with powerful features. Fedora includes proprietary software in its repos.
Trisquel is a distribution based on Ubunt. Unlike Ubuntu, it only ships free/libre software and a deblobbed kernel. As long as your hardware works without nonfree software, it makes for a great desktop, workstation, or server.