You actually need a product called a transcoder. This is built into most mid-level and better A/V receivers these days, but is not 'cheap' to find on its own as a product.
Composite (yellow) uses 1 75-ohm cable and they make cheap s-video to composite transcoders.
S-Video (round) uses 2 75-ohm cables and they make cheap s-video to composite transcoders
Component (red, green, blue) uses 3 75-ohm cables and I haven't seen much in the way of cheap transcoders, except A/V receivers.
You do not get a benefit out of using component video unless your original source material originates as component video. If it originates as s-video, then use s-video, you won't be unhappy with the results.