For me the best are "Boys over flowers", "You're beautiful", "My love from another star", "To the beautiful you", "Mischievous kiss"(this is a Japanese drama), "Playfull kiss"( the Korean version of mischievous kiss). These are really good and also funny dramas. I hope you like them. ^^
I think She was pretty or Boys over flowers is good if your starting out.
although I really like Gu family book, my love from the stars, emergency couple and dream high (not the 2nd one).
as for variety shows, I HIGHLY recommend running man.
my favorite korean movie is "A werewolf boy" and its SOO good.