Linux Mint comes with default Gnome and MATE desktop environment. To install an additional K desktop environment (KDE):
sudo apt-get install kde-full
This is a huge package which is 1.4GB, this is the easiest way to install KDE if you have enough HDD spaces.
You can remove the kdm if you want, for me I preserve kdm but chose lightdm (Linux Mint default dm) as default.
To change lightdm background edit the file:
sudo gedit /etc/lightdm/unity-greeter.conf
Look for this line:
Change the absolute path to the path your preferred image (jpg or png) is located.