Welcome to the forums galute.
I know how I would do this project, but I've been using various programs for this type of thing for many years, and the process would not be perfectly straightforward for anyone just starting.
I'll list the programs that I would use, but there are many different tools for this, and not everyone would follow the same path. You'll lose the original menus by the way.
I'd break encryption with AnyDVD in the background, and then use DVDShrink in ReAuthor mode to rip each individual episode to the hard drive. Each episode would be saved as a separate dvd-video. Make sure to use NO Compression in DVDShrink as you rip.
I would then import the episodes into DVDLab Pro, which is a dvd authoring program. This will let me build a new dvd with the episodes I want and a menu to select them when playing on a stand alone dvd player.
Lab Pro is an expensive program, but there is a free trial that is fully functional. A free alternative, though much less capable, is DVDStyler. It will not import the small dvd-videos you get from Shrink directly. You'd have to run each one through Vob2Mpg first. Make sure to set DVDStyler correctly...make an NTSC dvd if you are in the US. Also set it to not re-encode the video since it is already compliant to dvd specifications.
Of the tools I've mentioned only DVDLab Pro and AnyDVD are commercial programs. Both have free trials. AnyDVD may not be necessary if your tv program dvd has only CSS encryption. DVDShrink can break CSS by itself, but not anything more advanced.