Huh. 
Either Giant Gila or Indestructible Man was my first viewing. I’d seen the promos a time or two and my friends described it a bit further, so I wasn’t exactly going in cold. I don’t willingly hate-watch shows. (If you’re stuck watching something unappealing just to placate the person next to you, that’s different.) So it’s good we hit it off right away, or I might not have gone back.
I recently rewatched Operation Double 007 and I think that would make a good intro episode for some people. Every one is familiar with the James Bond movies, so they would already understand what this movie was aiming for. They would get the gimmick of Sean Connery’s little brother as the star and the inclusion of some familiar faces from the Bond films. The movie itself (as edited for MST3K) is actually kind of fun to watch. The riffs are funny throughout, starting with their mocking of the bombastic theme song sung by that Shirley Bassey wannabe.
One point against it as an intro episode is that one of the host segments features a visit from Torgo, so that would be a baffling sketch to the uninitiated.
Depending on your audience, weird/wacky may backfire. I showed my boyfriend Overdrawn at the Memory Bank and Space Mutiny, and they fell pretty flat with him. He still watches with me sometimes (he knows how comforting this show is for me, so sometimes he asks if I want to put it on when I’m having a rough day), and has told me he prefers episodes like Kitten with a Whip, Avalanche, and Wild Rebels, because they “feel like real movies.”
We used the shorts to hook friends of ours. We knew we’d won them over when our friend laughed so hard at “A Date with Your Family,” his drink came out his nose.
One from each era;
The Crawling Eye because it’s the first and sets up the premise.
Gamera
Sinister Urge
Deathstalker
Giant Spider Invasion
Carnival Magic
I must admit, many of the are favorites but what better way to introduce someone than showing them your own choices?