Composite is the worst connection you can use!! So avoid if at all possible.
The order of connections from best to worst are:
HDMI
DVI
VGA
Component
RGB scart
S-Video
Composite
If you have Sky+ then S-Video is your best bet (assuming the PJ doesn't have scart)
If you have a DVD recorder, then they usually have scart in/component out capability which works reasonably well. Otherwise, as mentioned, a scart - component converter is a good option although brand new these converters cost around £70.
Games consoles are available with component cables which offer the best connection route and computers will work via VGA or DVI or even S-Video.
Your best bet with a projector is to invest in Sky HD in my opinion. Once you've witnessed HD on an 8ft screen, ordinary TV looks rubbish!!
If that all sounds too expensive, then look for a projector that has RGB scart socketry such as the Infocus In74 or the Panasonic AE900 to name but two. This way, you have the best and most direct route from TV/VCR to projector.
Good luck!