not familiar with his work, what are his best movies?
"Spring, Summer, Fall, Winter and Spring" and "3-Iron" are his most mainstream movies. I own both on DVD. They are both pretty good. "3-Iron" is probably a good one to see with your girl.
Other than those two there's:
"Bad Guy" - Woman publicly humiliates pimp, who has a crush on her; pimp gets revenge by manipulating her into a life of prostitution all the while watching her behind a two-way mirror.
"The Isle" - I haven't seen this one since the first time I watched it many years ago. I forgot what exactly it is about. There's a fisherman and a woman, and I remember the last scene in the movie is unusual but interesting. I definitely need to re-visit this one, as many people I've talked to consider this one to be his best (probably mostly arthouse movie fans.)
"Samaritan Girl" - Two girls are best friends. One is a prostitute. The other later decides to become a prostitute in order to try and understand her friend.
"The Bow" - Old man who lives on a fishing boat takes care of little girl he finds lost; plans to marry her when she turns 17; story begins when she is approaching her 17th birthday. In the meantime, she becomes interested in a young guy who sometimes fishes off the boat.
"Address Unknown" - I still need to watch this one. I've been putting it off for years. I've heard others say that this one is his best.
"Time" - Man and woman in relationship; she has low self-esteem; leaves him to change her face. He searches for her. Stuff happens. This one has an interesting ending.
These are the only ones I remember off the top of my head. He has a few others. As an introduction to Kim Ki-Duk, I'd say watch one of the first two I mentioned. They are probably a little more palatable in getting to know this director's style.