My Girlfriend is a Gumiho
Boys over flowers, and it's one of my favorites.
My First Korean drama was You're beautiful and Boys over Flowers (I watched them at the same time) BUT what really got me addicted would be the kdrama Good Doctor. I just happened to watch them on netflix and I got severely addicted. 
It was King2Hearts. And this is my favorite drama until today. :3
My Girl and/or Full House, remember watching both of them not that far apart so not quite sure which one it was and thinking at the time that My Girl was so hilarious while Full House was so dramatically romantic. 
Boys Over Flowers XD
I'm not sure but I think it was You're beautiful. tho I didn't realy like it
It was Full House. I loved Rain, started watching it and was entranced because it was so different from anything I'd ever seen before. A whole new world. An amazing experience.

(And then I watched a few other Dramas and noticed how awful and clichéd Full House really was. But it still has a special place in my heart. ;))
My first will be You're Beautiful :)
My first drama was Full House with Rain. I watched some of its episode on TV and I was in love with its theme song Unmyung <3
But I consider You're Beautiful my first drama cause it's the first I completed and loved :D