Hey there, I'm not that sure about your request, so you want dramas about all three (school, music, love) or just those categories?
Well either way, I can tots help you with taiwanese since I've seen alot. For Jap not so much since I just started as well. Please bare with me.
Taiwanese:
So firstly since you want to start on taiwanese dramas I think you should watch the 'classics' back when Taiwanese dramas were the bomb, basically during their best time.
- Autumn Concerto (2009) --> this is a true classic about love, fate, revenge and will honestly bring tears to your eyes.
- Prince turns into frog (2005) --> definitely a classic as well and it has all the clique settings but back then those weren't clique.
- My Lucky star (2007) --> Love and revenge involving jewellery and significance.
So these are three of my personal favourites and they're honestly some of the best taiwanese dramas so you should definitely check them out first.
For your categories, I'll just put down the ones that are good/famous.
School:
The only one I can remember now is the taiwanese version of 'Playful kiss', if you've seen the k-version. The taiwanese one is actually the oldest one.
- It started with a kiss (There is also season2 called: "They kissed again")
- Hana Kimi --> this is also a manga/anime remake, the k-version's called 'To the beautiful you'"
Music:
Taiwanese dramas don't have alot of music ones, though even if there is I might not know either since I don't remember favour this genre.
The only one I remember so far is called 'Fabulous Boy's which is the taiwanese remake of 'You're beautiful'
Love:
Since this topic is basically everything, I'll just give you some general good ones over the years.
- Love keeps going (2011) Pretty good one, 13 eps I think
- Pleasantly surprised (2014) this is has cooking factors and I think is a pretty good one in recent years
So far just go with these.
As for Jap dramas, I haven't seen much so I can't help you. :(
