I have used three Linux distributions: Ubuntu, Arch, and Debian. Here are my thoughts on the strengths and weaknesses of each.
Ubuntu
For a newcomer to Linux, Ubuntu is a natural choice. Canonical, the company behind Ubuntu, is a business, and as a business it is in their best interest to make Linux installation a no brainer. All drivers are included in the image and a live CD will allow you to experience Ubuntu without even installing the software. This allows you to determine if the distribution will work with your hardware, and test drive some of the applications. Once installed you will find all the features you expect from a mature desktop operating system. With a large user base, someone has probably already found a fix to problems you may experience.
Users migrating to Linux, myself included, are often migrating for the purpose of privacy and control. I don’t want to pay $1000 for a computer and then have to get Microsoft’s permission to use it. Meanwhile every keystroke is logged and my search queries a catalogued at headquarters. By signing up with Ubuntu, you are in for a similar experience. Desktop search pipes your queries to Amazon and the Ubuntu software manager will annoy you with advertisements for non-free crapware. Once you have become comfortable with Linux using Ubuntu, it is time to move on.
Arch
I thought I wanted a minimalist system, so I committed to Arch and the I3 window manager. Arch is a great system for someone who wants to learn Linux inside out. Nothing is preconfigured, forcing you to learn the intricasies of the configuration files. Most users will be hard core programmers - you have to be to deal with installation and configuration - so all problems have been encountered and solutions explicitly provided. I never had an Arch problem I couldn’t solve from reading the wiki. One quirk (feature?) of Arch is the rolling releases. When installing packages, you almost always need to run a system upgrade. 99% of the time this completes without problems, but occasionally, for example 2013-06-03 the file system directory layout was changed and a significant effort had to be invested in completing the upgrade. “Always read the Arch news before upgrading” - Arch is thoroughly and expertly documented, but this requires religious devotion.
The problem with Arch is that it requires a lot of work and time. Everything needs to be configured. For example, if you plug in a USB stick, nothing happens unless you configured auto-mount. I quickly came to realize that I don’t want to be a Linux guru, I just want to use Linux to get things done. That is what led me to Debian.
Debian
Debian is the distribution on which many other distributions (including Ubuntu) are built. Debian has the reputation for stability, with major releases occurring about every 2 years. Releases make use of well tested applications, sometimes a version or two behind what is currently available, to guarantee stability. Debian’s package manager is field tested and shared by many other distributions. Most software written for Linux will have an installation package for Debian. As I usually buy older computers with less memory, I use the minimalist Xfce window manager. Xfce has a clean layout, doesn’t install a lot of unnecessary software, yet provides the essentials you would expect in a modern window manager. There is a Debian installer that defaults to using Xfce as the window manager. I have been using Debian for a couple of years now and can report that I have encountered no issues that would prevent the average user from switching from Windows or Apple to Linux. The one exception would be Microsoft Office file compatibility. LibreOffice does a good job, but complex documents may not render properly.