Yes, HDMI to HDTV
Use HDMI for as much as possible, really.
Auto-calibration is helpful but not necessary.
Amazon (etc.) is a fine place to shop too, along with crutchfield. Actually, you should visit the crutchfield site to learn more about what you've asked me above . They have some useful diagrams and info. About.com is another place you can glean some more of the basics. Start slow, research/read a lot, and then pull the trigger on your purchase.