I have a SONY Wide Screen Projection TV with a million plug-in connectors on its back. I also have a DVD Player/Video Cassette Recorder. What connections must I make to play back DVD's & Tapes and to record? I am on Cable. Thanks for your help.

It depends on what your cable, DVD and TV support. There are basically 5 types of connections to consider:

Coax
Composite
S-Video
Component
HDMI

In that order. So you use the best quality connection available. You want to run the highest quality the Cable box outputs to the highest quality the DVD accepts, then run the highest quality output from the DVD to the equivalent input on the TV.