I understand your need to do that, but there are more than a couple of decades worth of episodes to see. Besides which, you’re going to have to skip a lot since many of the older ones are missing. Plus, not all of them have been put onto DVD yet. You might wait a really long time for that. I’m still waiting for some stories from the 3rd Doctor era to come out on DVD.
And, while I love Old Who, you have to take it in the context of the time it was written/filmed. New Who definitely has been updated and modernized well. Old Who is sort of a different creature compared to New Who, while still embracing the old show’s history.
I would also suggest Firefly but give it a chance if you don’t like it at first. It took me two tries before I went past the first episode but I found I loved it.
A personal preference, I would suggest The Twilight Zone but it isn’t for everyone. Some people can’t get past the hokey FX (which I can understand) and since it was on for so long there are some poor episodes but the good ones can be great.
DS9 was also good but like others said it should probably be watched in conjunction with TNG.
The X-Files is one of those few shows where the Monster of the Week episodes outclassed the arc episodes. I would suggest watching the first season to get a feel for the show and then use an episode guide to pick and choose the ones that sound interesting.