Camera for live feed-transfer to external monitor in adjacent room?
A Raspberry Pi might be what you are looking for.  It is a credit card sized Arm based computer running Raspbian (a Debian variant), and at $25 it may even be cheaper than buying several adapters.

You could simply attach a web cam to the Pi and attach the monitor or TV via HDMI or Component out.  To get to VGA you will need a converter which you can get for about $30.