Linux apps aren't picky: they'll take any system as it comes
The third factor in our trio is how well the desktop of your choice is supported. In some ways this is a chicken-and-egg question for newcomers since most won't know which desktop they want to use.
Pretty much any Linux application can be installed on any Linux system, at least in theory. That means any desktop can be installed with any distro, but in the real world it doesn't always work out quite that smoothly. For example, the Cinnamon desktop is a relatively new desktop interface developed by the same people who created Mint Linux, which means Cinnamon is nicely integrated with the rest of Mint. That doesn't mean you can't install Cinnamon on Fedora or Arch. You can and people do, but it will most likely be a bit trickier and finding solutions to your problems can be more difficult since fewer users will be using your particular setup. That's why, to stick with the Cinnamon example, it would make more sense to use Mint if you really want to use Cinnamon.
All of the distros I've mentioned ship with a default desktop that the distro has tweaked to work best with the rest of its tools. If you're just starting out I suggest sticking with the default desktop, which means, for example, if you download Fedora you'll end up a GNOME user. Grab OpenSuSE and you'll end up a KDE user. Install Ubuntu and you'll be a Unity user. Opt for Mint and you'll likely end up with the MATE or Cinnamon desktops.
That doesn't mean you're stuck with them, though. There's a flavor of Ubuntu for KDE fans; ditto for KDE on Fedora. You can also install GNOME on Mint and pretty much any other combination of distros and desktops, but until you get more comfortable, stick with what's on the default live CD.
These criteria are by no means the only things to look at when choosing a Linux distro, but they should make a good framework to start your investigation.
Beyond these, it’s also worth considering if you’re going to still need Windows apps. Some distros integrate better with virtual machines and WINE than others. For example, it's not hard to make Adobe Photoshop (the lack of which is frequently cited as a stumbling block to adopting Linux) run almost like a native application in Ubuntu (and by extension Mint, which is based on Ubuntu).
If you're installing Linux for friends or family, you'll likely want something that's as close to Windows as possible to minimise any potential confusion. In that case OpenSuSE may be the best choice since it mimics the Windows start button and task bar quite nicely (as will any KDE desktop, but OpenSuSE does a particularly nice job).
If you're installing Linux on a family computer you may want to consider Fedora, which has good support for the Sugar desktop, a desktop environment geared toward children (Sugar is what ships with the One Laptop Per Child machines).
If all of this is overwhelming, here's my advice: if you've never installed or used Linux before, start with Mint Linux and use the MATE desktop. Installation is easy and most hardware should work right out of the box, which will get you up and running in no time. Most of the software you'll need is installed by default - web browsers, office suite, photo editors and music players are all included - and finding more apps is a breeze with Mint's software center. The MATE desktop also sticks with a familiar paradigm of mouse-driven menus.
If you want something a bit different, give Ubuntu Linux a try. The Unity desktop is a departure from the familiar world of Windows (or even most other Linux desktops), but once you wrap your head around it, it works quite well - especially if you're a fan of keyboard shortcuts. Like Mint, the installation and setup process are simple and in most cases all your hardware should work right out of the box.
Anyone planning to primarily use Linux to write software or develop web applications will likely be quite happy with Fedora, which does a good job of shipping up-to-date developer tools like Python, Ruby (and Rails) and web servers like Apache. The software installer may not be the best, but the command line Yum installer works just fine so long as you're comfortable with the terminal.
OpenSuSE is also a great choice for most users. Historically it has been particularly good in business settings, but thanks to a really well done KDE release, it makes an excellent choice for just about any situation.
Jumping from Windows or Mac to Linux is an unsettling experience, as you exit the predictable, pre-packaged world to one of choice and where support doesn’t come from a phone call or a Genius Bar.
The reward is a system that gives you the choice to obtain a system that reflects you and your way of working. Making the right choice means thinking carefully about how you work and what you do, and tuning out the noise of those in rival distro camps who think they’ve got the monopoly on the correct Linux choice. ®