I agree with 3ngin33r, it depends on what the person likes. But I think the easiest way is to choose something with multiple genres.
For my friends who liked mainly romance, I choose "You who came from the stars" (SF + romantic comedy). Just after one episode of this, which they really liked, I tried to let them discover "Kill Me Heal Me" (romantic comedy + mystery). But this one couldn't get them interested because they had a hard time differentiating the actors. Whereas in YWCFS, it was way easier.
For my parents, after seven years of struggling, I finally succeded in making them watch a whole drama with "I Hear Your Voice" (SF + mystery + romance + comedy). They needed a very good mystery plot with some humour to be interested.
If you want to find a period drama, I would suggest to not choose one set in old time, or at least not fully. Queen In Hyun's man could be a good idea because it's a time-travel drama with many alternations between the two time periods. You can also try Bridal Mask, which is set around 1940 I think. It's not that much into the past but you begin to have the feel of an ancient period drama.