I went with a Fedora install, because I like the ease of the RPM/YUM combo and that is what I am used to. These instructions will probably work for you on another Linux Distro, but there might be some tweaks that you have to go through to get everything the way you want it.
My base install is pretty much Fedora installed with X11 packages and nothing else. I uncheck all the other groups. This brings my install down to about one gigabyte right now. I am working to continue to whittle out the packages that the box isn't going to need. I am thinking that I might build a kickstart file for this so when/if I do, I will post it here.
Once you get up into the OS, go ahead and upgrade it to the lastest packages. That should just make things go smoother later when you are installing VLC and setting it up.
VideoLan Client setup for this is pretty easy. Really all we have to do is add a couple lines to the yum config and then tell it to install. You should only have to add one repo to your yum.conf and that one is Freshrpms.net. Start by downloading the freshrpms-release file and installing it:
rpm -Uvh freshrpms-release-1.1-1.fc.noarch.rpm
Once that is done you can import the GPG key and install the VideoLan-Client. A simple:
yum install videolan-client
Should get it installed for you. You can now play around with connecting it to your streams and making sure everything is working for you.
Frontend at bootup
So like I said at the beginning I need these machines to come up and just start playing the video streams without and user input or without the user even having the ability to manipulate the machines. So to accomplish that goal I need to get the machine up with X running, but I don't want to start a window manager or anything.