What is FOSS?
If you're new to Linux and open-source software, it will be helpful for you to understand what "free, open-source software" (FOSS) means. FOSS software is free to use (often referred to as the "free beer" aspect); and its source code (the human-language code before it's compiled into binary code that a computer can use) is also freely available to view, modify, and integrate into other projects, subject to the terms of whatever license it's been released under. Typically this includes releasing any changes you made to the public under the same license.
Within this context, "non-free" software usually means software that is free to use, but whose source code is not made public. It can also mean software that you dohave to pay to use; but paid software is more often referred to as "commercial" or "proprietary" software.Some people refuse to use non-free software. Others are happy to use it. Linux leaves that choice to you. Similarly, some Linux distributions do not include non-free software (you can install it yourself if you want, however). Others do, especially non-free device drivers.
Personally, I think it would make it a lot easier and less confusing all around if we just used the term "closed-source" or "free-to-use" rather than "non-free." But no one ever asked for my opinion.
A "repository" (or "repo") is a location from which the system can download software. Every distribution has one or more "official" repositories curated by the distribution's maintainers. You are free to add other repositories if you like; but the software they contain may or may not be stable, may or may not work properly on your system, may or may not be legal to use in your jurisdiction, and may even be malicious in some cases. So when adding repositories, do so with caution.
Desktop Linux Distributions
Strictly speaking, Linux refers to the Linux kernel, which is the core of the operating system. It interacts directly with the hardware, manages all of its resources, and makes them available to other software and applications. A Linux distribution is the Linux kernel plus a great deal of other software selected by the distribution's maintainers to create a complete operating system, usually tailored to a specific purpose (file server, Web server, workstation, etc.).
There are hundreds of Linux distributions, but a handful of them account for the bulk of user share in the desktop space. Most of these are built on one of the following three distributions, which themselves are not dependent on any other distributions:
Debian is a 100 percent FOSS distribution with a strong emphasis on stability. Debian itself has a popular desktop version prized for its stability and the absolute absence of non-free code. It's also the base for many popular derivative distributions (most of which are not so insistent about avoiding non-free software).
Red Hat is a company best known for Red Hat Enterprise Linux (RHEL), a commercial server distribution that is almost all FOSS and to which Red Hat is a major contributor. Red Hat tenaciously guards its trademark and a few proprietary components of RHEL, but releases the source code for the rest. It's the basis for many FOSS and commercial derivative distributions.
Arch Linux is an independent minimalist Linux distribution that focuses on structural simplicity, stability, and correctness of code. It expects the user to become competent in the shell (analogous to the "command line" in Windows) and lacks official, GUI-based tools for most configuration settings. It is a fast, powerful, stable Linux distribution; but it's not an easy one. There are a few derivative distributions, most notably Manjaro, that attempt to make it easier for novices to install and use.
For the sake of writing with some authority, I'm going to limit my opinions to Linux distributions I have installed and at least tested out within the past year or so. I'll mention a few others, as well, but without any recommendations other than where you can find them.
Debian and Debian-Derived Distributions
Debian is a 100 percent FOSS distribution that is prized for its stability, its extensive package repositories, and its complete avoidance of non-free software in the main distribution. (The do host some non-free software, mainly device drivers, on their servers, however.) The Debian stable branch also avoids any software that has not met Debian's testing standards, which are, in my opinion, the most stringent in Linux land. If what you crave above all else is stability, Debian is probably what you're looking for.
Debian and its derivatives use the apt (Advanced Packaging Tool) and the deb package format to install and update packages.
Ubuntu is based on Debian, but includes some Ubuntu-specific packages as well as some packages imported from Debian's "unstable" branch. Consequently, an Ubuntu default installation will include a wider variety of software than a Debian default installation will, making it a popular Linux choice for families. There's something for everyone in Ubuntu. But it also means that the likelihood of the occasional buggy app slipping through is much greater than it would be with a pure Debian installation.
Ubuntu doesn't install non-free software (such as non-free device drivers) by default, but does offer that option both during and after installation.
Linux Mint is based on both Debian and Ubuntu and was designed from the ground up as a desktop distribution. The default installation includes a smaller set of packages than Ubuntu and emphasizes office and productivity applications selected to enable the user to do productive work. Because these kinds of applications tend to be quite mature, they also tend to be less buggy than some of the software in a default Ubuntu system. Because of this, I tend to recommend Mint over Ubuntu for adult users who just want a stable desktop computer and who don't care about things like games and toys.
Linux Mint optionally installs non-free software and multimedia codecs that may be patent-protected in some countries.
KDE Neon is built on an Ubuntu base with a focus on making the latest and greatest KDE feature available to users, while updating the rest of the system normally through the Ubuntu repositories. It differs from the Kubuntu fork of Ubuntu mainly in its installing fewer applications by default and in its focus on KDE applications. If you love KDE, this might be the distro for you.
Red Hat-Derived (or Compatible)
Fedora is the upstream source of Red Hat Enterprise Linux. It is primarily a FOSS system, but it does offer to install certain non-free firmware. Its repositories do not contain any software that might present patent problems. (Users are free, however, to install and use additional repositories if they live in countries where the patents do not apply.)
Fedora is, in my opinion, the most innovation-focused of the major distributions, occasionally at the cost of some buggy applications sneaking through. It also offers many spins for users who prefer desktop environments other than the default Gnome.
As with all Red Hat-based distributions, software installation and updates use the RPM package management system.
Mageia is sometimes called the best-kept secret in Linux. It's a highly-polished continuation of the now-defunct Mandriva project, which previously had been known as "Mandrake" until the company lost a ridiculous trademark lawsuit alleging that a Linux distribution called Mandrake could be confused with a clown named Mandrake.
If you're familiar with Microsoft Windows and want a polished, stable desktop Linux with practically no learning curve, it's hard to beat Mageia Linux with KDE. Mageia, like its predecessors, is a purpose-built desktop operating system that comes with graphical tools to do just about everything, especially in the KDE version.
Mageia provides live image .iso files with KDE, Gnome or Xfce that you can write to a USB drive to test the distribution. The full version also includes additional desktop environments including LXDE, Mate, Razorqt, and others. Non-free software is installed optionally.
CentOS is actually more popular as a robust and reliable server operating system. It powers a significant chunk of the World Wide Web, including the server hosting this site. It can also be installed as a desktop system, however, and maintains live CD versions featuring either the Gnome or KDE desktop environment. These can be downloaded from any of the project's mirrors.
My favorite role for CentOS with a graphical desktop is when I mainly need a robust server operating system, but I also need some graphical capability, such as for a video server or camera controller. For a desktop Linux computer, I lean more toward distributions that were purpose-built for the desktop.
Distributions I Haven't Tried in a While
OpenSUSE is a Red Hat-derived distribution targeted mainly at developers and system administrators. They have a very strong open-source focus.
Arch Linux is an independent, fast, and (in its default configuration) lightweight distribution more geared toward advanced Linux enthusiasts who feel comfortable taking a building-block approach to creating an operating system than to ordinary users who just want a computer that works. The installation is notoriously difficult and, in my opinion, impossible for most new users to successfully complete. On the other hand, if you really want to learn Linux, then this might be the distro for you.Manjaro is based on Arch and is an attempt to bring its power and stability to users who aren't already Linux gurus. The notoriously-difficult installation is simplified, and packages are more thoroughly tested for stability so as to reduce frustration for users if they malfunction. The online communities also tend to be more patient with newbie questions. One might call Manjaro the "kinder, gentler Arch Linux" distribution.
Clear Linux is an Intel-sponsored containerized Linux designed mainly for cloud implementation on Intel hardware. It can also be installed on bare metal computers running recent Intel processors and GPU's. Packages are distributed as "bundles" rather than individually, and everything runs in a container. You can also install other applications using Flatpacks. The entire system updates as a whole on a more-or-less continual basis, but at file level rather than package level. I tried it out a while ago and found it fast and stable, but I didn't use it in real-life work long enough to form a qualified opinion about it.
I encourage you to visit the above (or other) Linux distributions to learn more about them. Most offer "Live" versions that can run from a bootable USB stick so you can see how it likes your computer's hardware and whether you like the user experience before you commit to installing it on your computer's hard drive. I strong advise you to do just that before installing Linux. If bandwidth caps aren't an issue, for you, I suggest that you try multiple distributions before you decide which one you (and more importantly, your computer) like best.
The next page deal with Linux Desktop environments<.a>. Because the desktop environment is what you'll be interacting with most of the time, I suggest you give it a read if you're not already familiar with them.