The resolution of the image should be exactly the same as the resolution of the output device if viewing in full screen.
So if you have an 800x600 projector, convert your image to 800x600 (or within those confines - 800x500 is fine, for example).
The DPI is meaningless.
What you don't want to happen is to have the projector/TV etc rescale your image for you - you need to do that ahead of time.
Also, ideally you want a digital connection between the computer and the output device (DVI -> HDMI for example).
Finally, you need to check the colour and other adjustments on the output device. Again, ideally, you would calibrate it but if you can't, try setting everything back to default. Any changes you may have made on the plasma to improve the image for viewing televsion is probably working against obtaining the best quality for still images.
Finally, since your TV or projector will at best provide an sRGB (or thereabouts) gamut, you need to ensure your images are in such a space.