EDIT:
a reply to Vidya's comment below. The following assumes you already have a graphical desktop installed on your VM, KDE, Gnome, or what not.
I like this connection to be shown in a window of its own, which I can resize, move, fold, or maximize as need be. So I use Xephyr: on your home computer running any Linux, first you will have to install it,
sudo apt-get install xserver-xephyr
(this command is suitable for Debian and derivatives, if you use a diffent distro you will have to use a suitable package manager), then you start it with
Xephyr -ac -br :1 -resizeable &
(please notice the capital X here, not in the install package), where the important options are :1 (this is what your new display will be called) and resizeable, which allows you to modify the window as per your wishes.
Now you can start your remote session to your server with:
DISPLAY=:1.0 ssh -Y [email protected]
and, once you are inside the virtual machine a command suitable to your display manager, like startkde (if you have KDE), or startx and so on will start your graphical session inside the Xephyr window. If you want, before starting the graphical session, you can just start a simple applications like xeyes which is very fast to load, and should open in the Xephyr window. When you are done, just kill the Xephyr window, that's it.