Basically, what stories could you give to someone who's not familiar with "classic" continuity and have it make sense and be enjoyable? Something like an All-Star Superman or Dark Knight Returns.

I ask not because I think the character hasn't produced good or important stories, but because the more I think about it, the more it seems Peter's best and most-remembered stories are either parts of long form runs ("If This be My Destiny" for Ditko's tenure. for example) or play off that continuity in significant ways (Kraven's Last Hunt, for instance, requires knowledge of both Kraven and Peter's marriage to MJ).

Imo, I think the best candidates are some of the more famous single issues like "The Kid Who Collects Spider-Man" and Life Story. The former can sometimes suffer from outdated storytelling conventions but can serve as succinct insights into Peter Parker and his world; the latter fits "classic" continuity into a relatively discreet package and is basically a crash course in Peter's development through the decades. Honorable mention to "The Night Gwen Stacy Died": the iconography is definitely a part of the broader cultural consciousness, but I'm not sure Gwen's death plays the same in a post-Spider-Gwen world.