how to install gui for debian
To install GUI (Graphical User Interface) for debian
Gnome
# apt-get install aptitude tasksel
# tasksel install gnome-desktop --new-install
KDE
# apt-get install kde-standard
XFCE
# apt-get install xfce4 xfce4-goodies thunar-archive-plugin
There are more options to choose from this page http://namhuy.net/1085/install-gui-on-debian-7-wheezy.html
The package in debian for the x window system is called "xserver-xorg-core", not "x-window-system-core" which would be your problem.
So you would install it with: apt-get install xserver-xorg-core gdm.
If you want your system to be light-weight I wouldn't go for GDM as a display manager as it really isn't very light. I'd suggest either LightDM or SLiM instead.
Lastly, you'll probably also want a Window Manager as the xserver on its own only gives you the windows, nothing more. An example of a light-weight window manager is Openbox.
See the debian wiki for details and examples:
http://wiki.debian.org/DisplayManager
http://wiki.debian.org/WindowManager
http://wiki.debian.org/Xorg
Just replace your previous second command or line with this one:
Previous commands:
$apt-get update
$apt-get install x-window-system-core gdm
New working commands:
$apt-get update
$apt-get install x-window-system-core gdm3