So, this is the best I can do, for now. I tried to respect as many main story arcs as I could for as many characters as I could. Some of my choices may not be immediately obvious, so I've included some explanations!
1. Welcome to the Hellmouth (obv)
2. Prophecy Girl (obv)
3. School Hard (need to introduce Spike and his relationship to Angel/Angelus)
4. Innocence (introduction of Angelus, plenty of discussion of the events of Surprise so we understand how he came about)
5. Becoming Pt 1 (for the flashbacks, and the introduction of the possibility of transforming Angelus back to Angel)
6. Becoming Pt 2 (obv)
7. Dead Man's Party (lots of talk about the fact that Buffy left and reactions to her homecoming)
8. Faith Hope and Trick (introduction of Faith, and rest of the gang finds out what really happened in Angel's mansion before Buffy left)
9. Bad Girls (we see Buffy and Faith's relationship at its best, and the accidental killing)
10. Choices (we learn that Faith is in with the Mayor and that she's not remorseful for the accident)
11. Grad Pt 2 (as important as Part 1 is, we can figure out what happened to Buffy, Faith, and Angel by watching Part 2--remember, this isn't a "best episodes" list, just being practical!)
12. Pangs (we learn that Spike was captured by The Initiative and that he's been chipped. Xanya. Angel checks in)
13. New Moon Rising (we learn about what happened with Oz, and about the relationship between Willow/Tara)
14. No Place Like Home (very important plot points: Buffy discovers Dawn's identity, the Dagon Sphere, introduction of Glory, Joyce's illness addressed)
15. Forever (as important as "The Body" is, we don't need to see it to know what happens. Also in this episode, more insight into the status of Bangel when Angel visits, plus some new insight into Spike as he mourns Joyce, helps Dawn. Also, we see that Xander and Anya are happy together)
16. Tough Love (we learn what Spike did for Buffy and Dawn in Intervention, Glory mind-sucks Tara, first glimpse at vengeful Willow)
17. The Gift
18. Flooded (we learn that Buffy was brought back and how, plus Giles' reaction to it, introduction of the Trio)
19. Grave (we learn what happened to Tara and what Willow has done--and the consequences that follow. We learn about "the bathroom scene," Spike's remorse, and his quest to find his soul.)
20. Never Leave Me (we learn about the First, about Buffy's faith in Spike, about the Watcher's Council, discussion of Andrew, Jonathan, and what happened at the seal)
21. Touched (Faith is back, potentials are here, Buffy has lost her footing, Spike helps her get it back. We see Xander and Anya reunited. Caleb/ First stuff addressed)
22. Chosen
Yikes! It's pretty depressing to think of our beloved Btvs as a chopped up mess of recaps--but I like a challenge! One thing I couldn't quite fit in was the mention of Xander leaving Anya at the altar--I don't think it's discussed in any of the episodes I used. If anything, in "Never Leave Me," Xander makes it seem like Anya left *him* and not the other way around, when he's talking to Andrew. Gar.