If you want to watch K-dramas, I'd recommend Secret Garden, Coffee Prince, City Hunter, You're Beautiful and Personal Taste for example.
But if you're in the mood for a j-drama, my recommendations would be Hanazakari no Kimitachi e, Nodame Cantabile, Soredemo Ikite Yuku, Buzzer Beat, Hana Yori Dango, Proposal Daisakusen, Kimi wa Petto, Rich Man Poor Woman and Tatta Hitotsu no Koi.
I haven't watched a huge amount of dramas, but I've seen those and I personally liked them a lot. ^^
Wow! Hello~ Welcome to MDL, Misa-chanx. :)
I'd recommend the Korean Movie "Sunny" and the Japanese Movie "Paradise Kiss". These two are my favorites. ^^ I suggest you go first with the light ones before the melodramatic ones ;)