Recommendations for Jdramas

So I'd like to watch more Jdrama, but don't know what to watch. I feel like a dummy because I'm part Japanese yet I've only seen about three Jdramas and I'd also like to talk to my grandma about all the actors and stuff because she seems like she wants me to like it too?? So I'd like to start with the really popular ones, if you guys could suggest any. Like if I was talking about Korean ones (I'm trying to make this make sense, please bare with me), what would be the Descendants of the Sun of Japan? What are the must-watch Japanese dramas that will help me enter the Japanese drama fandom?

Hi, as far as I know, prime-time drama ratings in Japan have sunk even lower than in South Korea these days. To get something that was really a big mainstream phenomenon (if any), I think you need to go back to the '90s. Tokyo Love Story, any drama that Takuya Kimura did in the '90s--I'm sure people more knowledgeable than me will give some recs.

If you're talking about new dramas, however, I'd second what @AnanyaS had recommended: We Married as a Job, which was really a major success and as close as a Japanese DotS that I can think of. Oh, and it even sparked a cultural phenomenon called the "Koi Dance" (look it up).

And since you mentioned about your grandmother and how you wanted to have something to talk about with her, what about trying some asadora? They're morning daily dramas, about 15-minute per episode. (Quite popular among women, and traditionally almost always enjoy high ratings.) The episode count is rather intimidating--but hey, they're short, and since they're made so that homemakers can watch them while doing chores, you can skip and fast-forward if some parts felt boring, without losing the gist of the story.

Asuko March!
Buzzer Beat
Kingyo Club
Limit
Nobuta Wo Produce
Siren
Hanazakari no Kimitachi e
Good Luck!!
Neko Zamurai

I agree with most of the recommendations already given! I most definitely second (and third, and fourth) Nigeru wa Haji da ga Yaku ni Tatsu, and I'll also add a couple of early-mid 2000s recs:

Tiger & Dragon (comedy) -- I found this hilarious, plus it focuses on rakugo which might be fun to share with your grandmother, if she would like you to know more about traditional Japanese entertainment~ (this is unrelated but I finally saw my first rakugo performance IRL this month--it was SO GOOD! if you haven't seen one already, I recommend it!)

One Million Stars Falling from the Sky (mystery, thriller, romance, tragedy) -- starts off a little slow but IMO it's worth a watch (and a rewatch ;D)