My first dramas were "when spring comes" and "Hello my Lady" both of which aren't famous or anything, but there were on the KBS World channel that me and my family "accidentally" got when we got the arabic satellite. Then when I missed a last episode of some drama, I started looking it up on the internet.. Thats when I got introduced to also Japanese & Taiwanese dramas :D I gave up Taiwanese after a while but come back to it sometimes, then I switch back and forth between Korean and Japanese ones (Among other things I watch Anime + British + Arabic + American/Canadian) depending on my mood. Gotta say it kinda changed my life :P (I see it in a good way others see it in a bad way)
Your experience is very similar to mine. When you first get introduced to this world, anything would do for you to get to know that world more, then you become more picky, but enjoying it all the same ;)
I've never seen a drama with more than 25 episodes. I am not sure if 28 hours of my life would be worth it or…
I've never watched an asian drama for more than 20 episodes... except "History of the Salaryman" which I felt cheated when it was extended so I never planned to watch this show but I promised a friend I'd try the first episode &... got so addicted that 22 episodes went by without me feeling it :P its both hard to watch and addicting at the same time ;)
This was one of the most amazing movies ever!! Tragic and sad, but captivating! Colourful! I dunno what to say to convince people to watch it!! Its really a movie that will be appreciated by all kinds of viewers
K-Drama 
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Your experience is very similar to mine. When you first get introduced to this world, anything would do for you to get to know that world more, then you become more picky, but enjoying it all the same ;)