I'd recommend Age of Youth because it really drew me in when I first started watching it.  Besides, there will be a season 2 coming out this year!

But if you want something lighter, cuter, funnier even (though it *might* get a little too much later on), Strong Woman Do Bong Soon is what you really should watch!
Age of Youth is REALLY GOOD!! 
and I second Drinking Solo~
Marriage, Not Dating!! That drama is realllly funny. I watched Chief Kim, Punch, and Do Bong Soon but I couldn't get myself to finish them.
Age of Youth, Strong Woman Do Bong Soon, Legend of the Blue Sea and Shopping King Louis
Girl, go for Falling for Innocence
and Shopping King Louis! :)
Chief Kim
The Greatest Love
Shopping King Louis
Rooftop Prince
Marriage, Not Dating
Shopping King Louis 
chief kim
chief kim
chief kim
chief kim
chief kim

The greatest love for comedy. I laughed so hard. The romance is good too.
Shopping King Louie because they were such an adorable couple.