Install a minimal X on Linux

apt-get install xinit i3 rxvt

i3 is the lightweight window manager
rxvt is the terminal
xinit gives you X windows and the famous "startx" command

To make i3 use your full screen resolution, create the file ~/.xinitrc and put the following there

xrandr --output Virtual1 --mode 1680x1050
exec i3

You may need to change the name "Virtual1" to something else. Use xrandr to list all the known windows (you first need to have X windows  running though)