The lightweight variants usually include alternatives for the bloated apps, e.g. Midori or others for Firefox, or Abiword not OpenOffice. If you are on a really low memory system, you can also use Google Docs. With 200 MB I find that Firefox is fine as long as you don't have too many apps, and use something like Crunchbang or U-Lite - although Xubuntu is billed as low memory it really isn't, and runs very slowly in 200 MB with a lot of swapping. Checking memory usage with htop is quite revealing.
SliTaz is an even lighter variant that looks promising as well. In all these cases you'll need to help the friend/relative get started, but at least Crunchbang and others provide live CDs and an easy install process - no different to standard Ubuntu in that case.
I'm counting a couple of running apps such as browser and word processor in the memory usage. Crunchbang and SliTaz clearly use way less than 200MB just to start up.
As for video, I found a 700 MHz PIII too slow for Youtube Flash videos, which is the key application for Joe Public. You are probably right about VNC not being optimal for video, but perhaps it would work OK for smaller Youtube-sized videos (not full screen) - I have used SSVNC logged into a remote system showing a webcam view from Skype and it does work over the Internet, using SSH over VNC, but not very well. I'm reasonably sure that smaller videos would work fine over 802.11g WiFi, but not SD or HD TV of course.