The best image you will get is by using a 15-pin SVGA cable between your LCD monitor and the computer. This is actually true of any display hooked to a computer.
Okay... well, DVI or HDMI may look a bit better... though not much typically.
So, out of your computer, run the 15-pin monitor cable directly to your LCD display. You can pick up long SVGA cables online including eBay for not much money and they will look WAY better than converting computer resolutions to composite.
Many computers have video cards on them that already will convert to composite... they look HORRIBLE hooked to a TV though, everyone complains.
If your PC only has one SVGA output, you can either split it using a splitter which isn't overly expensive... or better (in my opinion) would be to get a second video card for your computer and dedicate the second video card for your LCD display. Less headaches, and more flexibility that way.