Look up a free program called Handbrake. It converts video files to mkv, mp4, and webM. It also handles subtitles. If you need mpeg only then this person's setup is too old. You can check wikiHow to convert files to mpeg.
I second the recommendation to get a media box or a cheap bluray player that has a usb slot. Burning dvds will be a pain in the ass because you have to manage file sizes, take time to burn the dvds, and you will end up with useless piles of plastic discs when you're done. Sharing one or two usb drives is much easier.
They still haven't fixed the Lemmy bug that can't handle "and" in post titles.