At work I use several older desktops for various functions. As in "older" I mean 2006 or so :) One system is used primarily for the internet if a customer needs internet access, another system is set up for a cheap live webcam to monitor outdoor premises, and so on.
In looking for an easy to install OS that is Ubuntu/Debian based I have had MUCH success with Linux Lite. Linux Lite is a beginner-friendly Linux distribution based on Ubuntu 14.04 LTS and featuring the Xfce desktop.
Linux Lite is delightfully lightweight and runs fast & responsive on our old computers which are single core Pentium 4 - 3.0Ghtz, with 2GB of memory. I have had problems in the past with graphics while installing Xubuntu or Lubuntu, but not so with Linux Lite.
A ton of time is also saved with pre-installed programs like VLC, LibreOffice, GIMP, Firefox, Steam, and Thunderbird.
It also has its own built in program called Lite Software which makes life super easy for you to install other useful apps including: Chrome browser, Chromium browser, Dropbox, Ubuntu Games Pack, Pidgin chat, Google Talk plugin, Java, KeePassX password manager, PlayOnLinux for windows games, Ubuntu Restricted Extras, Skype, TeamViewer, Deluge torrent app, OpenShot video editor, VirtualBox, and XBMC.
If you have older computers and other distros are not working out for you, definitely give Linux Lite a try!