Recommend my your Top 5 Dramas

Kazoku game

Nobuta wo Produce

Quiz show 2

Liar Game (beware of the cheese in this, over the top acting, but still compelling)

Code Blue all 3 seasons (movie coming in 2018)

Soo many many more but these 5 should get you started

Proposal Daisakusen & Special

Shitsuren Chocolatier

Legal High & SP

Legal High 2 & SP

Boku, Unmei no Hito desu

Kazoku Game, Liar Game and Nobuta wo produce were already mentionned, so I would suggest these five  (though there are numerous others I could have mentioned too). For a starter : 

- Maou, 

- Mother

- Hanzawa Naoki

- Tumbling,

- Quartet.

They are all excellent, not sure if it's good to begin with the best.

Million Yen Women

Ouroboros 

Rich Man, Poor Woman 

Hotaru no Hikari 

Romance:

1. Hana yori dango
2. Nodame Cantabile
3. Soratobu Kouhoushitsu
4. Buzzer Beat
5. Pride

Suspense:

1. Maou
2. Kazoku Game
3. Ryusei no Kizuna
4. N no tame ni
5. The Quiz show 2

And I second and highly recommend: 1 litre of tears

1. Mare (An asadora. Usually, Asadora tends to have a very high rating in Japan. About a girl who used to hate dream. Funny and heartwarming)

2. Nigeru Wa Haji Da ga yaku ni tatsu (Rom-com drama. It is very funny, and the ost song  and dance Koi by Hoshino Gen is very popular )

3. Kinkyu Torishirabeshitsu 1-2 (Crime, police drama)

4. Tenno no Ryoriban (someone already mentions it before. I think this is  one of the best projects by Takeru Satoh)

5. Doctor X (1-5) (Very popular in Japan. It has 5 seasons for a good reason. About a genius female surgeon who hates to be restricted by hospital policies and politics.  She does what she wants.) 

5.  Code Blue

4. Gokusen

3. Hero

2. Team Iryu Dragon

1. Doctor X