DVD if you want it in your possession. It seems like the idea of having movies stored in Clouds or by your cable provider is popular. But ya have to keep paying the bill to see the movies. When you die you have no movies to give your family. Unless they pay the bill.
Meh. I grew up with a VCR in my house. Lots of old tapes still lying around in a box somewhere. DVD/Blueray have their place I suppose. I liked being able to tape programmes off the television then record over them when finished. You can't do that with your fancy dvds as far as I am aware. More power if you like dvd but for this old fart I'll stick with what I grew up with.
DVR records from TV its digital and part of the cable converter. I think DVR can be bought stand alone too.