I'd approach this issue like this:
1. Get it working on the LAN first, and secure it. When you are happy that it works....
2. Forward the approriate port on your router
3. Set yourself up some way of tracking your dynamic IP - DynDNS for example.
I had some issues with Vinagre to the point I dropped it and used 'NX Client/Server' (http://www.nomachine.com/download.php
), but that was some time ago. As most of the machines I log in to are Windows (ironically) I tend to use the Gnome tsclient.
Good luck :-)