My book club did a Lisa See deep dive last year, so we had this list pinned. It's definitely: 1. 'Flower Net' (1997), 2. 'The Interior' (1999), 3. 'Dragon Bones' (2003), 4. 'Snow Flower and the Secret Fan' (2005), 5. 'Peony in Love' (2007), 6. 'Shanghai Girls' (2009), 7. 'Dreams of Joy' (2011), 8. 'China Dolls' (2014), 9. 'The Tea Girl of Hummingbird Lane' (2017), 10. 'The Island of Sea Women' (2019), 11. 'Lady Tan's Circle of Women' (2023). We read them in that order and it was a great experience.
Hmm, I'm not sure I agree with pushing 'Snow Flower' first just because it's popular. If your stated goal is following recurring characters, you should go straight to the source: 'Shanghai Girls'. Jumping in with a standalone might make you impatient if what you really want is a continuing saga. The emotional payoff in 'Dreams of Joy' relies entirely on the foundation built in the first book.
Treat those two as a single, long novel. Once you've finished that story, you'll know if you're invested in her writing enough to explore the other, unrelated books. They're all great, but they won't give you that 'what happens next' feeling.
Plot-wise, you won't be lost reading out of order. But theme-wise, you might miss a subtle progression. Her early books often focus on a woman in immediate, personal danger from a specific threat. Her later work expands to look at systemic family secrets, the dangers of technology, and the fragility of community. Seeing that expansion happen in real-time, book by book, is a study in how a writer's interests evolve with the culture.