There are four modern distros that I can recommend for someone in your situation.
For servers: Although these distros can be used for workstations, they are super stable (running only mature versions of software) and make great server OSes:
CentOS - This distro is designed for use in enterprise situations. It's very useful if you plan on, or think you may work with Red Hat Enterprise Linux in the future.
http://centos.org/ http://www.centos.org/docs/5/
Debian - A stable distro that uses only free
http://www.debian.org/intro/free software out of the box. There is also a "testing" version of Debian that you can use if you like the way Debian works, but want to use newer software. See
http://www.debian.org/releases/
Which one should you use? That depends on which workstation distro you want to use, as I will explain below.
Workstation distros: These distros Are designed mainly for workstation use and are less stable (Less mature, but still very usable) than the distros above.
Fedora: Uses the cutting edge of open source software to provide a super modern workstation distro. It has the best hardware support of any Linux distro I have seen. Great environment for developing Linux software as well.
http://fedoraproject.org/ http://docs.fedoraproject.org/en-US/index.html
Ubuntu: I have mixed feelings about Ubuntu. It is based on Debian. It is designed to make Linux easy to use for the average computer user. As such, it makes a great workstation distro. Every two releases they have what's called a long term support release. Which is supposed to be more stable than a standard Ubuntu release. However, the Ubuntu team seems to be more focused on usability and eye-candy than stability and hardware support. Even when using only LTS releases, I always seem to find a few nasty regressions or memory leaks and such. Because of this, I would only recommend it to those who are VERY accustomed to Windows or Mac OS and want as little change as possible. IMHO it is not suitable for medium to large size businesses.
http://www.ubuntu.com/ https://help.ubuntu.com/
Because Ubuntu is based on Debian, it uses the same package management system (apt & deb). So if you use ubuntu for your workstations, you should use Ubuntu server or Debian for your server OS.
The same rule applies for Fedora and CentOS. It uses a different package management system (yum&rpm).
There is also another distro that uses RPM & yum called OpenSUSE, but I don't have much experience with it.
http://www.opensuse.org/en/
Some books to read if you go the Ubuntu/Debian route:
https://www.amazon.com/Official-Ubuntu-Book-Benjamin-Mako/dp/0137081308/ http://apress.com/book/view/1590598202
And for CentOS/Fedora:
http://apress.com/book/view/1430219645
And a very good book on many Linux distros:
http://apress.com/book/view/1430219122
Choosing a distro is a bit like choosing a car; you need to find the best one to fit for your needs. Try all of these distros for a wile, read the documentation, install them, use them as if they were running on your production systems. Then make a choice.