Hi Susan C3. I agree, Reign of Assassins was terrific. It was great to see Michelle Yeoh "back in action" and Jung Woo-Sung was great as her suitor/husband.
Not sure exactly what you mean by culturally significant - are you looking for films portraying the culture and people, or films that focus on historical events? For me, just watching films made for the Chinese audience can teach you so much about the culture because the stories portray people living their lives within the culture - hope that makes sense.
The following links may help out with your search. The first is for "TimeoutHongKong". To celebrate the 100th anniversary of Hong Kong films, the Timeout film critic published a list of the 100 Greatest Hong Kong Films of all Time:
The next link is for LoveHKFilm.com. This site has reviews of current and past Chinese films as well as news about current and upcoming film releases and film industry news.
As for some suggestions for action films:
"Once Upon a Time in China I, II, and III" These films star Jet Li and have tremendous martial arts action.
"Policy Story I, II, and III" with Jackie Chan. Amazing stunts and action
"Hard-Boiled" with Chow Yun Fat and directed by John Woo (who produced Reign of Assassins). You can't go wrong with any films directed by John Woo and starring Chow Yun Fat, but if you have to choose one, this is it for most people. "The Killer" is my favorite, but the action sequences in "Hard Boiled" are beyond compare.
The above websites will also give you lots of great suggestions.