This is a small guide to hopefully help you settle on a certain GNU+Linux distribution. This guide is written because the question "which distro should I pick" comes up a lot, and a single reference document to picking a distro would be much more useful than trying to answer the question to each one individually.
Be aware that this is not a full, comprehensive guide. You should pick whatever distro you like, and don't be afraid to experiment a with other distros. If you feel like a distro should be mentioned, send in a MR on this repository.
Which distro should I pick for …?
The purpose of Linux Mint is to produce a modern, elegant and comfortable operating system which is both powerful and easy to use. It's made to work out of the box with full multimedia support while being easy to use. It is based on Ubuntu, hence comes with all the software that Ubuntu itself supports.
Lubuntu is a spin-off from Ubuntu. It comes with a graphical installer and sports the LXDE desktop environment, which is ment to be lightweight. LXDE by default comes with a taskbar, a "start" menu and desktop icons which should be pretty straight-forward to anyone coming from a Windows-like system.
Xubuntu is a spin-off from Ubuntu. Like Lubuntu, it comes with a graphical installer and the default UI is pretty similar to Windows.
The server release provides netinstall images in which you can choose what is installed at installation time like many other netinstall distros like Ubuntu.
A spin-off from Gentoo. Funtoo is against systemd, and uses OpenRC instead. Other than that, it is pretty similar to Gentoo nowadays.
Gentoo is often hailed as the go-to distribution if you want to customize everything. It has an advanced package system that uses so-called USE flags to indicate which features you want and which ones you don't. This brings along the downside of having to compile all your packages yourself, save for a very small set of packages which have -bin versions available (such as Firefox and LibreOffice).
Using the traditional installer, Mageia is very customizable, yet easy for beginners who are willing to read up on the documentation. All updates to the system are tested by the QA team, so it's a pretty safe bet for stability too. If you wish to do so, the installer can leave you with a system containing only free software.
This is the most minimal version of Ubuntu available. This means that you have a small starting base which you can setup completely to your liking. Ubuntu supports a PPA system to easily add in software that's missing from the main repositories. There's also a big community behind it which is usually pretty helpful and friendly.
A distribution based on Arch Linux. Since only a small part of Arch official packages are nonfree or contain nonfree components, there's no need for them to repackage everything. In their repos, you'll find Arch official packages, directly from its official repositories, minus the nonfree packages, plus their libre replacements, when possible.
A free distribution based on Debian.
The netinstaller for Debian is the most minimal version you can start out with. It's stable, produces a very small OS once done installing is incredibly stable. Be aware that Debian by default does not allow non-free software in the main repos, so not all hardware may be supported out of the box.
Lubuntu's LXDE desktop environment is made specifically to be usable on systems with low resources.
While not as lightweight as Lubuntu, it's lightweight enough to run on most machines. It's a little more polished than Lubuntu by default, but this is ofcourse subjective to your tastes.
Debian is often described as the most stable GNU+Linux distribution around. The release cycles are incredibly slow, which is a good thing when going for stability in general. Before packages hit the stable repositories, they have been thoroughly tested to make sure that they won't break anything.
Due to their extensive QA testing before pushing new changes, the distro is really stable, yet doesn't use packages as outdated as Debian stable.
Every distro can be customized to be Your Special Snowflake™. Just pick whatever distribution's package manager feels best to you, and start customizing everything you want different.
Why isn't … in this list?
Arch Linux doesn't provide anything special. People often claim it's "customizable", but it's no more customizable than Ubuntu itself. The community is also very unwelcoming to people who want to customize it beyond what the devs intended.
There's claims of it being "lightweight", but a debian netinstall is smaller than a base Arch Linux installation. This is mostly due to Arch Linux including development headers in all their packages, which is completely unneeded for a binary package distribution.
These are fine operating systems on themselves, but they are not GNU+Linux distributions, therefore they are not included in this list. If you want to try it out, the installation is about the same as Debian, but it comes with more up to date software and a great ports system, but hardware support is often not as great as GNU+Linux.
I've never used OpenSUSE nor do I know anyone who has ever done such a thing. Therefore I can't recommend it with a nice little description about it. If you have experience with it, and feel it should be included, please send in a merge request.
Everything not mentioned
It either doesn't fit the categories, or I just don't know about the distribution. I'd greatly appreciate any help in maintaining this list, and that includes suggestions for other distros in the list. You can have one added by sending in a MR on the repository.