Tall and well educated. Doesn't have to mean rich perse, but must have a strong position in society.
All other qualities in a men (funny, caring, nice guy) are icing on the cake.
That said, korean women are expected by society to get married at age 24-28 so if a korean women (or any other asian women for that matter) is still single after she turned 30 she will most likely drop her standards.
If you're canadian you're in luck too as it much easier for us koreans to get a visa in canada then in usa. Ofcourse it's best to avoid asian women who marry for a visa but the sad reality is that alot of korean want to get out of korea, because of stress and working conditions.
I hope my post helped.