First off, there are a fuck ton of K-Dramas. If it turns out you enjoy them, you will have a huge backlog of series to enjoy as well as plenty of new series each month.
The best way I can convey that they are good is that Korea is a very conservative country. Basically no sex, drugs and limited violence in their entertainment...and the shows are STILL good : ) The other thing I noted is that a K-Drama series typically last 16 1+ hour episodes where basically at the end, nothing really happened...and they're STILL entertaining : ) Around episode 8 of a series I find myself thinking everything and nothing happened and how the hell are there 8 more episodes left to watch but there are still more twists and turns ahead. Depending on the series, you can end up tearing up. There's a ton of crying in some series. The other thing about K-Dramas is that they don't unfold as predictably as you might first think at the start of the series.
I initially decided to watch some K-Drama because I figured I'd learn a little about Korean culture (and some Chinese modern day culture).
K-Dramas are the best IMO, but there are an endless supply of C-Dramas (Chinese) of which some can be good but no where near the quality of K-Dramas. K-Dramas have more music and higher budgets) I actually watched the C-Drama "Love Scenery" first because it caught my attention having an MMORPG being the mechanic where two people initially meet anonymously. The interesting part was the MMO parts were played out live action style.
There's quite a variety of K-Drama. First thing to mention is that while there are just a handful of them on Netflix and Apple TV, VIKI.COM https://www.viki.com/ is where you go to access all K-Drama, C-Drama, J-Drama and most other Asian drama and movies. There's a 7 day free trial and then either 4.99 or 9.99/month which is totally worth it if you end up enjoying K-Drama.
The K-drama Squid Game is currently the most watched series on Neflix in the US. That's a first. I haven't watched it yet but I hear it's good.
As with the 80's High School movies (Breakfast Club, Fast Times, Ferris, Pretty in Pink etc) I enjoy High School drama. With that said, I'd recommend watching True Beauty, which I believe is available on Apple TV or Viki. That will give you a good idea of what K-Drama is like. You need to get over any hang ups of guys wearing as much makeup as girls. That's just the way it is. While True Beauty IMO is a good intro into K-Drama, keep in mind it's high school, there are plenty of other genres.
Here are some recommendations from what I've watched: (most of the titles translate kind of corny sounding)
High School dramas:
True Beauty
My Strange Hero
Love Revolution
Best Mistake
When We Were Young (C-Drama)
A Love so Beautiful (C-Drama)
Romance/Comedy (ROMCOM)
Weightlifting Fairy Kim Bok Joo - best title ever and really good, don't ignore due to title!
Backstreet Rookie
Love Scenery (C-Drama) - higher than normal production values for a C-Drama
Yumi's Cells
More Adult/Series mix of drama/romance/some comedy
Guardian: The Lonely and Great God (a benchmark, highly rated series)
Uncontrollably Fond - great acting
Descendants of the Sun
Hotel Del Luna - Main female lead is IU, a famous Korean singer. amazing wardrobe changes like every 5 minutes. Decent but slow moving story.
K-Pop Related
Imitation
Dream High
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Resources:
VIKI.COM - one stop shop for K-drama and all other Asian drama (except for a couple Netflix exclusives)
MyDramaList.Com Great resource (like IMDB) to find other dramas with an actor you might like
I'd recommend watching these two:
True Beauty - High School ROMCOM with some deep drama parts. Many Kdramas are based off of webtoons. This is one of them.

Guardian: The lonley and Great God - Also known as "Goblin" but make sure you watch the right one with these actors:

Just a warning about Guardian and some other K-Dramas. A lot of times they have flashbacks to ancient history in the beginning but the main story takes place in present day. For that reason, a series like Guardian, I recommend watching at least 2 episodes to get a grip on what's going on.
Two K-Dramas I think are available on Netflix that are highly regarded but I haven't watched yet besides already mentoned Squid Game:
Crash Landing on You
What's Wrong with Secretary Kim
Other k-Dramas I've watched that were ok but 2nd tier
Love Alarm
So I married an Anti-Fan
Playful Kiss