The actual timeline is Movie 1 then Drama then Movie 2.  However, there are some things that don't actually match up between the stories of each.  Character introduction did happen in the first movie, but the lack of character introduction in the drama is actually used as a way to keep them kind of mysterious and is somewhat revealed later in the drama.  So you could watch the first movie and find stuff out, or you could watch the drama kind of like that part is a mystery and find out some later in the drama.  It's a little confusing to explain.  My personal opinion is to watch the drama first, then watch the movies if you want.  However, the movies are really different from the drama, so be aware of that in making your decision.