First, I am not a geek.
In the "old days" (i.e., just a couple of years ago) when movies came out on video cassettes, I had ONE unit which would allow me to accomplish what I wanted: 1. the ability to watch movies and 2. the ability to record a TV show on one channel while I watched another on another channel.
Nowadays, with movies on CDs, am I correct in thinking that what I need is a DVD/VCR?
Should I get a blu-ray DVD player?
Movies are not on CDs; they are a different packaged media, the dvd. The dvd has a physical size and visual appearance similar to the cd but they are totally different in technology.
Movies are produced on both standard dvd platform as well as blu-ray. Blu ray is a higher resolution and gives much better picture quality.
The above link will explain some of the differences between dvd and blu-ray.
There are dvd recording machines available commercially. There are also blu-ray recorders but they are very expensive.
There are also dvd/vcr combo players and recorders.
Therefore, you have many choices. But, remember, the vcr picture resolution quality is only 480 lines whereas HD video is 720 and 1020 and up. So, if picture quality is important to you it would be best to stick with dvd quality.
But your desire to record one channel and view another simultaneously will be a function of your cable provider and the equipment selected AND the coding of the program which may or may not allow off-air recording.
See the following link which explains the coding of record or non-record bit in the digital stream used with digital tv.
Your cable company would like to include in your package a digital recorder which uses HD recording for later playback of tv programs where all is stored on computer disc rather than on packaged media discs.
Hope this helps.