What originally stood out about them? Was it the character they played that you liked, or something about their looks? What stood out enough to make you follow them more than other actors and actresses that played characters you enjoyed in dramas? Do you see everything they are in, even if the plot doesn't appeal to you?

I first noticed Lee Min Ki  properly in Nell's the day before mv.He was playing a friend of main character who attempted suicide.he had no dialouge in mv but he still managed to convey all the feelings of a suicidal person just with his eyes and that moment i fell for him :)

As for Yoo Ah In first i loved his character in Secret Love Affair(i had seen him in different things before but i hadnt pay attention.After that i pretty much stalked him on tumblr then his acting sealed the deal for me <3
I had already seen quite a few dramas and liked a few actors, but as soon as soon as I saw Lee Joon Gi in the first episode of Arang and the Magistrate, I felt a completely different sort of appreciation. He was an awesome actor and was extremely handsome, but I fell absolutely in love with his character there.
At first I saw Ji Chang Wook in Healer and fell in love with the character he played. However he wasn't my favorite actor until I've seen him in Empress Ki. I had a love-hate relationship with the character he played but I loved how he was able to convey the feelings of such a complex character so realistic. I've noticed that he is able to pull of his character's development to perfection. Afterwards I''ve become curious about him. Not to mention that he looks very attractive xP
When I first saw Jun ji hyun in My Sassy Girl. She was just so natural in her acting yet she exuded so much charm that made me instantly love her. I guess it had something to do with her role in MSG as well.. Then I went on a binge and watched most of her movies and honestly, she didnt disappoint. She's got the talent and the looks. Also I love her personality, and the way she carries herself, she has a great personality without necessarily being loud or trying really hard to be funny etc. All in all, she is my favourite Korean actress and I have yet to see anyone as captivating as she is. 
 Emily:
When I first saw Jun ji hyun in My Sassy Girl. She was just so natural in her acting yet she exuded so much charm that made me instantly love her. I guess it had something to do with her role in MSG as well.. Then I went on a binge and watched most of her movies and honestly, she didnt disappoint. She's got the talent and the looks. Also I love her personality, and the way she carries herself, she has a great personality without necessarily being loud or trying really hard to be funny etc. All in all, she is my favourite Korean actress and I have yet to see anyone as captivating as she is. 

I have to agree, though rather late reply :)  It was also my first korean movie I saw.   Jun Ji Hyun was excellent and once you have seen an actor or actress you like you tend to seek out other k-dramas or movies they have appeared in.  In the case of Jun Ji Hyun, Windstruck, IL Mare, You Came From The Stars, Legend of the Blue Sea etc... If you are looking for people who are captivating I would also include Jun Do Yeon and Kim Sun Ah to the list, as for me, they have also left an impression. Jun Do Yeon is charismatic and is convincing in her performances, whilst Kim Sun Ah reminds me of Jun Ji Hyun in her expressions and in her acting.