I would start off with something that's preconfigured to just work out of the box, like Manjaro. Manjaro also has a great community, that's not full of BS like the forums of Ubuntu and derivatives, and that's not "elitist" like Debian, Fedora or Arch fora.
Manjaro is still not at version 1.0, but it's already one of the most popular distros out there for private desktop use.
Manjaro is based on Arch, which is a really nice distro because of the choices that Arch makes: bleeding edge, low bloatware, high community involvement. Arch is the ultimate "indie" distro, but they tend to be rather technical because they don't mind pushing updates out before testing for breakage. Manjaro fixes this by offering stable updates, still in a rolling release model (which is the way to go in my opinion), but they usually wait a couple of days before pushing the arch updates (except security updates of course) through to their repos, to make sure that there is no breakage.
Advanced users might get into hardened systems, server installs, specialized distros, etc... and might then find Manjaro insufficient, but new users really should join the Manjaro hype in my opinion, it's well worth the time saved and the community info absorbed. All codecs are preinstalled, flash is preinstalled, everything is preconfigured, everything just works, you can easily switch between proprietary and open source graphics drivers with a simple GUI application, you can easily switch between kernels with a simple GUI application, etc... everything is made incredibly simple, whilst still retaining all the features out of the box. There is no other distro in existance for the moment that offers the same out of the box experience and great community to get started with linux.
If you're going to use the PC for work in a hybrid environment (meaning that there will also be software consoles like Windows, XBox, OSX systems, or commercial media/file servers or clients in the network), you might want to go for OpenSuSE or Mageia. Especially OpenSuSE is very much on the right track for the moment. Since a lot of the development funding for OpenSuSE comes from the proceeds of SuSE licenses sold by Microsoft (Microsoft is the largest commercial linux vendor in the world, and they sell those licenses for 50% premium price, and that money flows back into OpenSuSE development basically, yeah it's odd how that goes, Microsoft pays for OpenSuSE linux development while laying off it's own MS-Windows developers...), SuSE takes particular care in providing extensive Microsoft compatibility. And not only compatibility with Microsoft, but also Xen is available out of the box, etc...
The benefits of OpenSuSE are that first of all, it's an RPM distro. There is nothing really that can compare to the packaging quality and the software management security and practicality of the RPM system. That's why enterprises use RPM distros. The RPM software packaging system provides huge time and bandwidth savings, and a lot more tools for software management (like selective package install history with selective undo functions, very handy if you run into trouble, or like advanced interactive conflict management if packages do not work together well, it's dealt with in a preemptive stage, instead of having to figure out what's wrong after having installed a package, etc...)
With GKH as maintainer of OpenSuSE Tumbleweed and Factory, the rolling release and super bleeding edge repos, these have really come a long way, and are pretty much the best of linux right now, regardless of distro. And that's just it, SuSE offers what's called the "build service": they provide all of their packages to all distros, you can actually get SuSE packages for DEB distros, for Arch, or as source. You can also use the build service to make your own custom distro online, and try it out on an Amazon server first, before even downloading it. It's great service, that is available nowhere else.
Another benefit of OpenSuSE is Yast, which is a one-stop control panel that allows for easy GUI based access to all settings and configurations, including software installs. Those software installs are also made very easy, because Yast uses something that's called "Yast 1-click install", which allows you to search OpenSuSE for a certain package, for instance, non-OSS codecs, and then click on the Yast 1-click install button in the corresponding page on the OpenSuSE site in your browser, and it will take care of all the aspects of the installation (adding repos, adding security keys, adding packages, adding dependencies and libraries, and preemptively solving possible conflicts, for you). This is also unique to OpenSuSE.
Mageia has a separate install interface that contains a similar one-click system for the most common installations, but not online, it's a local application. It's not as refined and powerful as Yast in OpenSuSE, but therefore, Mageia is based on Mandrake, and still has the tools from Mandrake, amongst which drakxconf, which is a life saver for inexperienced users that like to experiment and have broken their x server doing that, because it gives you user friendly pseudo-GUI access to all major settings right from the terminal. ROSA is very similar, mainly for people that speak Russian, there is a benefit in using ROSA over Mageia.
All of these distros are made by worldwide communities, but don't have their headquarters in Gitmo/5-Eyes nations, so there is less stress as far as using them is concerned. Sadly, this is also an increasingly important factor. Manjaro is based in Germany, but the main maintainers are from Austria, Germany and France. OpenSuSE is from Germany, the parent company SuSE is also from Germany, and the parent company of SuSE is now from the UK, not from the US any more, but SuSE has always been very independent, even when it was owned by Corel, and then Novell, and then Attachmate. Mageia is based in France. ROSA is based in Russia.
Debian is the largest indie distro, based in North-America but also very global. Debian is very conservative, even in their development branches. Don't use Debian stable on a desktop, you'll miss out of too many modern features. Debian stable is the ideal distro for quick setting up and maintaining servers, because it very secure, conservative (you don't have to learn any new stuff and don't have to upgrade much), and guarantees very reliable basic functionality. On a desktop, you can use Debian Unstable or even better, Debian Sid, but at that point, you might as well go for Arch, because the low maintenance is not there any more, and Arch is more flexible, has a better community documentation, and offers better performance, plus, and this is a huge benefit of everything based on Arch - including Manjaro for that matter -, Arch has the AUR, the Arch User repository, which is arguably the most extensive collection of software on the face of the planet. Pretty much anything you'd like is in there, regardless of how rare or crazy. Even SuSE Factory or Sabayon doesn't have as large a software collection as the AUR.
Another option that is often left out of the equation, is to install the most popular linux distro in the history of mankind: Android. Android is available as Android-x86, thanks to the Chinese Intel developer team that makes that happen. It works very well on most x86 hardware, and Android is the most user friendly distro ever, and has a lot of free to use tools that aren't excluded from access to proprietary formats because everyone needs Google, and Google makes Android, ...
Android works really fast, and allows for great productivity. And if you usually play Android games, which is ever more a thing because those are the most played and most popular games in the world, having Android on an x86 machine with keyboard and mouse or gaming controller offers a better experience for a lot of games, and offers a smoother graphical experience in many cases. Android also handles all kinds of documents and information very well, and has exemplary integration of all kinds of cloud services.
A very viable alternative to that, is using CrOS aka ChromeOS. This is a Gentoo-based linux distro made by Google, which contains a lot of non-OSS additions. One of the recent additions, is the ability to run Android applications right in the Chrome/Chromium browser. This includes all of the Android games and applications for Android by Microsoft, Adobe, Autodesk, etc... but at the same time, the solidity and performance of the Gentoo base is still there, and the system is definitely more robust than Android.
With Google moving towards better encryption and more security, and the Chrome browser using the latest linux kernel features that enable advanced sandboxing, this might become a thing in the near future, as ever more people get a cheaper Chromebook instead of a traditional laptop, and Android games are becoming ever more popular (the Android gaming market is exponentially larger than the PC gaming market already).
There is so much choice in linux distros, and the people that enter the linux realm right now, don't have to put up with the old linux ways any more. You don't have to get frustrated by Ubuntu or other low quality overhyped linux products any more to make your way into a next-gen computing experience. There are still benefits for techy people that really want every feature, the ultimate privacy, security and performance, and have the hardware to satisfy their needs, but it's not something that is absolutely required any more for regular users that just want a great experience out of the box.
The linux world is much larger than you would imagine, and it really is the platform for the ultimate computing experience, regardless of the type of user.