JDRAMA FOR A BEGINNER

Hello Yusuf,It's a good idea to try japanese drama, they have all a special athmosphere really interesting, I could advise you these dramas, they are really popular, they are all 2000's :
- http://mydramalist.com/2988-nobuta-wo-produce (school, friendship, suspense), my favorite.
- http://mydramalist.com/44-kurosagi (action, crime, suspense)
- http://mydramalist.com/570-life (school, friendship, psychological)
- http://mydramalist.com/40-liar-game (suspense, psychological)
- http://mydramalist.com/2-1-litre-no-namida (tragedy, school, family)
I hope you enjoy watching ;)

Romance with no love triangle:

Soratobu Kouhoshitsu
Mars
Nigeru wa Haji da ga Yaku ni Tatsu  
Nodame Cantabile
Sekai Ichi Muzukashii Koi
Tatta Hitotsu no Koi
Boku, Unmei no hito desu

And must watch of other genres (no romance or not the main focus)

DRAMA
1 litre of tears - the story of a hig hschool student with spinocerebral degeneration
Byakuyako – this is a very intense drama about 2 people that met since childhood and develop a strange relationship in which both of them are united by a serious of crimes
Koizora
Taiyou no kisetsu – a romance drama but with melo in it
Soredemo, ikite yuku – this drama is also very heavy and it’s about a man whose sister is killed and the the killer’s sister who meets and falls in love with that man
Sekai no Chuushin de, Ai wo sakebu


COMEDY
Atashinchi no Danshi -
Hanazakari no Kimitachi e – reverse harem a girl crossdressing and living in a boys school
Ouran High school host club – reverse harem a girl crossdressing so she can be part of the school’s host club
Mei-chan no shitsuji
My Boss, my hero – this drama is hilarious and it’s about a yakuza that has to go back to highschool in order to get his high school diploma, but he has to keep his yakuza status a secret

SLICE OF LIFE
My girl – it’s a drama of a man that suddenly finds out he has a daughter and has to live wit her.
GTO – If you liked Dragon Zakura you’ll like this one and the following one (Gokusen) It’s about teachers and troublesome students
Gokusen
Dragon Zakura

SUSPENSE
Maou – the best suspense drama ever!
The quiz show 2 – it’s about a Quiz show were they ask the contestants very personal questions in order to reveal their deepest secrets
N no tame ni – it’s about a group of friends that are united due to a double assassination and they hide who the killer is 
Ryusei no Kizuna – a revenge drama about 3 siblings who look for the killer of their parents before the statute of limitations ends
Liar Game – it’s about a game that involves lying a deception in order to win
Kazoku game – it’s a psychological drama about a teacher and a family and his strange ways of teaching
Kurosagi – it’s about a swindler who targets swindlers due to his personal vendetta

SPORTS
H2 – baseball and romance united in a story about  life
Tumbling – a group of boys who bond through tumbling and find a dream to follow
Yowakutemo Katemasu – a different kind of underdog drama about a baseball team who challenges winning a baseball game with new strategies involving their weakness
Rookies - a baseball drama about a high school team.

Hanazakari no Kimitachi e (2007) (Comedy, Drama, Friendship, Manga, Romance, School, Sports) is a classic, and doesn't really look old. It has been done in Korean though so if you saw the To the Beautiful You it is the same concept but is far less dramatic than it's Korean remake.

My first drama was Bloody Monday; a bit of action and suspense 
but all those recommended earlier are very good too, especially Freeter, ie wo kao, ryusei no kizuna,Kurosagi, Maou, my boss my hero, Byakuyakou and koizora 

Article covering this topic here on MDL >>  http://mydramalist.com/article/2016/07/17/so-youre-new-to-j-dramas