Get the cheapest HDMI cable. All this gold plating and whatever is just marketing bull****. The quality of the cable matters little for digital transmission. I used the cheapest, thin headphone extension cable for digital audio without problems.
I buy cables from
http://www.ramelectronics.net/, they have cheap but good cables.
The HD video delivered by "100% digital" cable companies is usually over-compressed to save spectrum and full of compression artifacts. If you want real HD get a BlueRay player or download HD movies from the net. Still the HD channels look much better than standard TV but nowhere as good as Blue Ray.
You hook up the coax cable to the cable box then connect the box to the TV (and your audio system). You can use regular RCA (Red, White, Yellow) or SVHS cables but they're analog so if the box has HDMI then definitely use it.
HDMI cable carries both digital video and digital multichannel sound. So you need just one HDMI cable to hookup a cable box to a TV. You may need another HDMI or a SPDIF (digital audio) cable if you want to feed the digital audio to your AV receiver. If you have multiple HDMI sources and your AV receiver supports HDMI switching you will, of course, need more cables.
Adam