There should be two sets of 3 cable component (Pb, Pr, Y) ports. Use them for both set top boxes, matching color for color. (sat & cable) If you have digital HDMI ports you want to use them for the service you watch most. Same goes for the DVD player. The VCR will work best with an S-Video cable. Those single yellow video ports are good for a camera or an old game box.
Coax is the worst connection method. Single yellow is next to last. S-Video is better, Component is best. Digital DVI/HDMI is the best for digital devices.
You would benefit from an inexpensive home theater receiver. Along with Dolby 5.1 surround sound you get multiple component inputs with a single component output to the set. I've seen good receivers with speakers for $150 and up.