JDramas are like art students..
They are singular, unique & quirky, but they got depth that only few people can appreciate, comprehend & embrace. From the way i see it, no matter what the genre is, doramas are divided into two types of project, either they go full on loud & chaotic, so you would want to just suspend reality for a while & just enjoy it. Or they do it with little to no lines at all, you would find yourselves think & feel so much, and even reflect about your own life while watching.
Since you seem entirely new to Jdramaland, i'd suggest you to kick off with some J-movies first, just to get the feeling of how characters in J-dramas usually roll. Although most Jdramas usually consist of 10 episodes, if one is not used to their pace, people would quickly label them as 'awkward' or 'draggy'.
But, if you're someone who enjoy tv series than movies, than i'd probably should also let you know that, almost all J-dramas, except for the ones done by Netflix, share this nearly identical non cinema look filter. I read somewhere online it has some thing to do with budget provided by the tv station. Having said that, if you found the well made ones, their script quality would remain tight nonetheless.
I recommend Unnatural & Miu 404 for comedy-crime genre, also Ichikei's Crow for legal-comedy section.
House of Ninjas for spy-action genre, this one is on Netflix. (one of the best Doramas i've seen in many many years)
For romantic comedy, i got Nodame Cantabile & From Five to Nine (the comedy part of this one in particular can only be thoroughly enjoyed by open minded people, otherwise you would most def dislike the male lead character).
And when you've eventually been exposed to enough Dorama and are finally used to its comedic timing & pattern, then maybe you're ready for some straight up pure, solid comedy of Dorama in Hanazakari no Kimitachi e & Fuben na Benriya .
^^