Love Me If You Dare e u w
Legend of Lu Zhen (really good plus with the cutest actress as the lead.)
Battle of Changsha (if you want a very realistic drama, REALISTIC, really.)
Nirvana in Fire (full of battle of the wits, really good.. very BRILLIANT)
The Journey of Flower (i personally think there are some scene w/c doesn't make sense but idk, it still got my attention, A LOT of attention)
Lady & Liar (too cliched tho--the story line is,  but will get your attention.)
Sound of the Desert (GREAT, just GREAT. it's really good--you'll love the main guy <3 )

Below are some of the dramas I (remembered) enjoyed before.
Boss and Me
My Sunshine

You should also try:
Love Me if You Dare
Scarlet Heart
(they are really popular! though personally, I didn't like both--not done with Scarlet tho)
I have seen Love Me If You Dare and it was really good , it became my first Chinese drama ,( its mix of genres more of detective type ).
I also have prepared this little competition, there are many good Chinese drama on the list which you can use as a reference (mostly are modern) I hope you all take a look and if possible vote against your least favorite drama there.

Masterpiece of Asian Dramas
Well I just started watching some too and am probably late anywayz hahaha
but I guess these would do:

Legend of Concubine Zhen Huan

good af, pretty easy to understand & not too much of a culture shock
like some of the historical/period drama stuffs I tried to start hahahaha
(for example journey of flower that got mentioned earlier
it was just too much for me to handle with that fantasy stuffs)

Sound of the Desert
does not seem too bad either at least up to this point (ep 15 basically)

 Battle of Changsha tho I have yet to watch it (onhold at ep 2 lmao)
because subtitle issues I ran to when I tried to watch it first time
but it seemed good tho

Nirvana in Fire as well but I found myself not understanding a shit
so I wanted to watch something easier first and then get back to it

...why did it turn out to be historical list tho hahaha

I find the historical stuff to be the best:

Battle Of Changsha
Nirvana In Fire
Lady & Liar
Prince of Lan Ling
Disguiser


If you want pure romance, you probably want to watch taiwanese drama:

Hi My Sweetheart
It started with a kiss
Back to 1989
In Time With You

Enjoy :)
Mainland China:
The Disguiser
The Battle of Changsha
Nirvana in Fire
Wu Xin: The Monster Killer
Divorce Lawyers
Go Princess Go


Taiwan:
In A Good Way
An Innocent Mistake

:)