Oh man, this is a big question. You don't want to start off with something as terrible as Manos, even though it is one of the most popular episodes they have. And you also probably want to watch things in a certain order so that you're not bouncing around between Comedy Central Joel, CC Mike, and Sci Fi Mike episodes.
So I'm going to give you episodes that I think will help ease you into watching whole movies, get to know the characters, and will follow the time line. This will not be literally every important MST3K episode, nor will it give you all of the catch phrases that become popular throughout the series (you'll have to go back later to stuff like Women of the Prehistoric Planet to find Hi-Keeba!, for example), but I think this will give you the highlights pretty well.
My Recommendations (watch in this order if you really want to "get into MST"):
(Items in Bold are some of my all time favorites)
- Rocketship X-M (Season 2, Episode 1) - First TV's Frank, First Kevin Murphy Servo
[*]Godzilla vs. Megalon (Season 2, Episode 12)
[*]Cave Dwellers (Season 3, Episode 1)
[*]Pod People (Season 3, Episode 3)
- Manos, the Hands of Fate (Season 4, Episode 24)
- Mitchell (Season 5, Episode 12) - Last Joel Episode
- The Brain that Wouldn't Die (Season 5, Episode 13) - First Mike episode
- Sampson vs. the Vampire Women (Season 6, Episode 24) - Last TV's Frank episode
- MST3K: The Movie
- Night of the Blood Beast (Season 7, Episode 1) - First episode with Pearl as Main Character
[*]Laserblast (Season 7, Episode 6) - Last Dr. F. episode, last with Trace as Crow, last CC episode
- Revenge of the Creature (Season 8, Episode 1) - First Sci Fi ep, first with Professor Bobo, first with Bill as Crow
[*]Space Mutiny (Season 8, Episode 20)
- Time Chasers (Season 8, Episode 21)
[*]Werewolf (Season 9, Episode 4)
[*]The Final Sacrifice (Season 9, Episode 10)
- Soultaker (Season 10, Episode 1) - Special Guests!
- Diabolik (Season 10, Episode 13) - Final Episode
Again, this list is nowhere near exhaustive. I took out a lot of episodes I really, really love or would be considered classics (Gamera vs. Guiron 312, Santa Clause Conquers the Martians 321, Fugitive Alien 310, Santa Claus 521, Prince of Space 816, Puma Man 903, etc.) because I wanted to give you the big hitters. Season 8 has a story line that tries to matter, so I gave up and only put in the episodes that I think people really love after the first episode. I also kind of ignored Season 1 because I think of Classic MST3K beginning in Season 2.
If you get through that list, I can give you a number more that would be great to pick up things that reoccur throughout the series.