Hi, I watch mainly K-drama's and want to try some J-dramas for a change... I tried it before, but I don't know where to start and I pick the wrong J-dramas. last time I picked LIAR GAME, but that wasn't quite what I was looking for. it felt too much like a manga to me still. The one that I liked was Orange Days, but that is not what I am looking for at the moment... I want something that has a story, humor and great characters. something between serious and light in. chemistry and acting is also important ! no melos and no dying because of a sickness please. whether it is a romcom or suspense/thriller drama isn't important, as long as it contains the things I just pointed out.
please try this dramas they may be what you are looking for :D Hanakimi last Cinderella Yankee-kun to Megane-chan Gokusen 2,3
hımmm, I am not sure what your favorite genre is so for; high school genre: Nobuta Wo Produce (my personal recommendation), my boss my hero, Hana Yori Dango, Hana Kimi... revenge genre: hanzawa naoki (literally broke the records, but a little serious), Joker Yurusarezaru Sousakan, Kurosagi... casual life and romance genre: Watashi ga Renai Dekinai Riyuu , Love Shuffle (these two are my personal recommendations), Rich Man Poor Woman, Hotaru no Hikari (like anime) supernatural genre: SPEC series, Long Love Letter... Love genre: Tatta Hitotsu no Koi, Pride (well there is Kimura Takuya in it :) Old woman young man relationship genre: Kimi wa Petto, Anego... etc... lastly I shall recommend Last Friends, it is not light or funny, but it discusses love in every aspect which I see as a different genre from Korean dramas, so if you are looking for something different than the korean dramas this one could be a good choice
Kaeru no Oujo-sama is a good drama and also very underrated. If you're looking for something musical and uplifting, I really recommend it. It's not incredible or amazing or anything, but it gave me a very satisfied feeling after watching it, if that makes any sense.
Legal High is fantastic if you're looking for a comedy. Both Aragaki Yui and Sakai Masato are wonderful in it, they play off each other so well. Just be prepared for some really ridiculous cases!
Marumo no Okite is pretty good if you're looking for a family drama.
The Trick series is long but very funny (and ridiculous). It has three seasons and several specials and movies. I'm not sure if it would be up your alley, though. It has a pretty specific sense of humor that people either love or don't.

Out of what's on your PTW list but doesn't fit your criteria, I just wanted to say that Kazoku Game is absolutely AMAZING. However, only watch it if you are in the mood for a very serious drama. It has superb writing and a wonderful cast.
Piece is good but again, pretty serious. It has romance but the most interesting thing for me was the mystery.
Why not Nodame Cantabile,Yamada Tarou Monogatari and Ryusei no Kizuna? In my opinion,they have "a story, humor and great characters" Nodame Cantabile is funny,sweet and interesting. Yamada Tarou Monogatari is heartwarming and funny. Ryusei no Kizuna is serious but it has humor and interesting characters + an enigma These dramas are perfect for summer days.
For light comedies:
Reinoryokusha Odagiri Kyoko no Uso : this drama is very light, there are lots of funny moments + some heartwarming moments.

For detective/investigation/crime dramas:
Keizoku 2: SPEC : although this may be a bit like Liar Game, which, as you said, gives off manga vibes, it's a lot better than that. I think you should give this a try
Kagi no Kakatta Heya[/URL] : an investigation drama, not so serious but you will learn a lot
MR. BRAIN : same with the above drama, if someone's looking for a crime/mystery drama, I will surely recommend this one
BOSS : strong lead woman, lots of funny moments

[U]For medical drama:

Doctor X[/URL] : very addicting drama

[U]For revenge drama:

Maou : this drama is the Japanese version of The Devil(Korean), so you may choose which one to watch

*bolded those I think you will really like
I recently watched Last Cinderella and it was pretty good. You might like it too!
Dramas I really enjoyed and that might somewhat fit here, were:
Take Five ~ Oretachi wa Ai wo Nusumeru ka
Tumbling
and
Gokuaku Ganbo (this one is still airing, but so far I really enjoyed it)

I also want to second Nobuta Wo Produce and Kaeru no Oujo-sama :)
I second Rich Man Poor Woman and also recommend Last Cinderella. Although I admit the title originally put me off and the plot didn't particularly strike me as anything interesting, the characters in this drama are very well developed. It's a light drama without being slapstick comedy, and it's realistic without being heavy or melodramatic at all. There's the typical love triangle, but I grew so attached to the characters it didn't seem artificial or irritating. And the chemistry was great! Sakura (the female lead) may be off-putting at first, but she truly grew on me and turned out to be an unusual, attaching character. Miura Haruma acts very well, I think his character is one of the sexiest I've ever seen ;)