That machine is called a computer. http/www.techsupportalert.com/best-free-streaming-media-recorder.htm
After you record the program you can burn a DVD or just watch the file. Not legal to do but quite common.
Most people don't bother since streaming media is available to watch on demand whenever you want so burning a copy that you may never watch again only makes sense if you want to give that disc to someone else.
You can use KODI to stream almost any video online. That is semi legal since you are just using KODI to aggregate links rather than record.
OK. Guys - watch your language. @Cubs - putting "watch on DVD player" obviously kicked us toward "DVD burning and playing".
So, @Cubs: What kind of "DVD player" you have? Does it allow for external video source to be connected to?
The easiest solution would be to get a streaming stick like Roku, or one of myriad Android boxes. A lot depends on where you stream your movies from. Most of these boxes support Netflix, Amazon, YouTube, Hulu. Some of them support HBO Online.
If you're talking about the gray places to stream videos from, I would be reluctant to give any help.