I re-discovered the Dead a few years a go when I was having a bit of a spring clean and found an old box of cassettes, including a C90 of Without A Net that I'd taped from the original vinyl (which I no longer have). Not having a tape player, I found a CD copy on eBay dirt cheap, listened to it again for the first time in decades and thought man, this is actually quite good. A few months later I'd bought everything I could get my hands on, and now have quite a good collection. The Brent era is hit and miss for me, but that 1989-90 run of shows is solid gold. The 76-78 era is the real sweet-spot though.
And it's true, once you get into the Dead, it's hard to listen to anything else. They have taken up about 70%+ of my listening time since, and show no sign of stopping.
A single show that would convert a sceptic? Not possible. Even the best show will have Jerry forgetting the words or Donna wailing slightly out of tune. All that free-form jamming is an acquired taste. Expect to like the Dead despite the jams. Then, one day, you'll listen to a show in the right state of relaxation and that jam will carry you away. After that, you'll love the Dead because of the jams. It's music in it's purest form.