The best bet is to use cgi proxy given that the server is used to host that proxy alone.
If you are hosting other sites on it then you are better off using PHProxy. Glype can be considered as well but the thing is that the development of that script seems dead now.
I would recomend the use of the Glype proxy script with a customised template which makes the pfoxified pages look like a web browser window. To keep it private I would use a .htaccess file to password protect the proxy script. Glype is compatible with SSL and if I remember correctly there is also a plugin which makes it compatible with Youtube.