I would say it depends upon what genre the person enjoys the most. My gateway into both were historical/fantasy dramas which is my favorite genre, but a lot of people dislike historicals so that definitely wouldn't draw them in.
So, imo, by genre:
Mystery/Thriller:
Cdramas: Reset or Under the Skin
Kdramas: Flower of Evil (it was my family's gateway since their favorite genre is mystery) or Black Out, depending upon their interest in romance.
Historical + historical/fantasy:
Cdramas: Unless they're a big fan of period drama, probably a mini is best. I'd say A Dream like the True Love or A Familiar Stranger. If they like the genre An Ancient Love Song, Blossom, New Life Begins, or Love between Fairy and Devil. For Republican Era Be Your Knight or Fall in Love.
Kdramas: The Tale of Nokdu, Love in the Moonlight, The Haunted Palace, or My Dearest
Fantasy not historical:
Cdramas: Golden House Hidden Love (for something sweet and light) or Twelve Letters (for something heavy). If they love romantasy novels and want something bonkers and unique Affinity.
Kdramas: Lovely Runner, W, or Happiness
Romance/Rom-com:
Cdramas: Put Your Head on My Shoulder, Lovely Us, Time and Him Are Just Right, When I Fly Towards You or Since I Met U (for sweet) or My Lethal Man (for a bit more edge)
Kdramas: Dali & Cocky Prince, My Sweet Mobster, or What's Wrong with Secretary Kim
Slice of Life:
Cdramas: Go Ahead or Reborn
Kdramas: Just Between Lovers or At a Distance, Spring Is Green