The premise and writing is great... and then it goes downhill.
I've seen both the anime and manga, and for quite some time preferred the manga greatly over the anime. I liked how the manga delved deeper into the emotions of the characters than the anime, and how every character of the zodiac was introduced. The anime stops around volume eight of the manga, before Rin and Kureno are introduced. Now that's my only issue with the anime and I strongly prefer it to the manga.
The two mediums have basically the same plot, although the anime wraps up differently (and more openly) than the manga. I grew up with this series, and as a young teenager didn't really have the life experience to connect with many of the characters. Now in my late teens, I've gone back and re-read and re-watched the series and connected far more than before. The fandom tends to overlook much of the backstory of the characters and focus on the gorgeous cast. Whenever I recommend the anime now, I emphasize that parts are tough to get through, and that people with a history of emotional abuse will likely be triggered by certain scenes.
Natsuki Takaya is an incredible writer and knows how to make her audience connect with the characters wonderfully. The series as a whole is very uplifting with the addition of Tohru Honda, the optimistic naive-yet-wise-beyond-her-years girl who is brought into the secret world of the Sohma family. The Sohmas have a curse that directly affects 14 of the family members. When stressed or hugged by a member of the opposite sex, 12 of them turn into their respective zodiac animal, the 13th is the cat whose been shunned by the rest, and the 14th takes on the role of God.
For the first 11 volumes of the manga, Tohru focuses on being there for the members of the family and healing them to the best of her ability. For the remainder of the series, the focus switches to breaking the curse. New non-cursed characters are added (none of which are particularly interesting in comparison to the Sohmas), revelations about characters' genders are made, and we find out that certain characters just sleep around a lot to manipulate everyone. It's a major, major case of Cerebus Syndrome
. (Plus the art quality declines in spades. You literally can not tell some of the characters apart in the manga.)
Watch the anime. It doesn't wrap up nicely, but its tone is consistent.