The cables with red,green,blue connectors are called "component" cables, capable of 480i,480p,720p,1080i formats.
"Composite" is the older single yellow connector cable, only capable of 480i SD format.
If your sources (cable box and dvd) and HDTV support HDMI then HDMI is the best to try if there are no compatbility issues. If your cable box model doesn't have HDMI you might ask your cable company if they have another model (maybe an HD DVR) that does support HDMI.
If a source doesn't have HDMI, it might have the older DVI output which is like HDMI but only video and there are DVI to HDMI cables available, however it would require an additional red/white stereo audio cable as well in that case.
If HDMI or DVI is not available on a source unit, if component (red/green/blue connectors) is available, it could be used but it also requires a separate red/white audio cable.
Component is an analog signal and not quite as "pure" as the digital signal available with HDMI and DVI. The red/white stereo audio cable is also an analog signal. With HDMI both video and audio are provided on a single cable and both are digital signals, its the newest most advanced format.
I personally have an HDTV hooked up to a cable box with HDMI and a upconverting DVD player with HDMI. I got the HDMI cables for low prices from monoprice (a forum sponsor) and they worked great with my new Panasonic TH-46PX80U plasma HDTV.