I've been thinking of stepping into the Star Trek rabbit hole. I've literally never seen an entire episode. Should I start with the original series? TNG? Is there maybe a list of episodes I can skip and not miss anything like there is for The X-Files and Babylon 5?
TNG would be a good starting point--just be aware that Season 1 has some weak episodes. There are 'critical path' guides if you want to avoid the weaker episodes, but honestly I'd just say watch the whole thing. TNG very much set the tone and established what Trek is in the modern era. It has a great cast, and its episodes can be really throught-provoking. It's a true classic.
From there, DS9 or TOS (the original series) would be a good next step; DS9 becomes much more narratively focused than other Trek shows, with episode-to-episode arcs and storylines, and TOS is, of course, the series that started it all. Either would be a good choice... and as dated as TOS is, it really is amazing how watchable it is, even nowadays. DS9, however, has some staff that cross over to become regulars from TNG, which will make it more familiar and it is far and away the darkest take on Star Trek.
The Trek movies (pre-Star trek '09) , Enterprise, and Voyager would be the other things worth watching, in that order. The movies have a very different feel than the shows. Enterprise is the series that killed Star Trek, but I've heard it got good in the last few seasons. Voyager was just really badly written overall, filled with plot contrivances and inconsistent characters, which makes it the worst Star Trek series by a fair margin... until the new movies.