Plot: This will be a general overview and what I like or dislike about each Book of the avatar series.
Book 1: Water --> I think Water is a good intro for the world of the Avatar. It works for introducing the series universe as a whole; explaining bending, what the avatar is, who the main characters are and what the war/major conflict is. However, everything pales in comparison to later Books/Seasons outside of specific episodes and the ending. For example, Zhao is a weak villain in comparison to say Azula, Zuko hasn't become conflicted, the Gaang has no Toph and hasn't begun to develop their characters yet. On a whole it works as a solid new TV show, but it has so much further to go by the time you reach the end.
Book 2: Earth --> This book is considered the Ur-Example of a well-written animated show. It is usually people's favorite Book due to a number of factors. These factors include: The prowess and competence of Azula, the way she ends the season is insane for any show; Long Feng & the Dai Li who are brainwashing dissenters; the concept of Ba Sing Se's class system, the introduction of Toph, Aang's difficulties with earthbending, Zuko's internal conflicts between Iroh and Azula's ideals, Appa's trials and tribulations, a whole slew of intriguing characters: the aforementioned, Bumi, Wan Shi Tong, sandbenders, and Mai & Ty Lee. There is also a lot of world-building in this season as the Earth Kingdom showcases a variety of perspectives and Aang develops more spirituality with Guru/Buddha sessions. It is my favorite season of the whole series for the ending alone and really the height of Avatar's well-written seasons.
Book 3: Fire --> This and the last book of Korra are the hardest books for me to place because while everything is wrapped up nicely they feel like they shouldn't be. That's primarily because while this is a series filled with grey characters it's still a kids' show that needs to have a happy ending. Fire is not a bad book, it's just that Earth had an ending that was unexpected, but sensible. Anyways, what I like most about Fire is how much more we learn about Ozai and his conflicted family. While I think Ozai is just a big bad without much depth his connections to his family: Iroh, Zuko, Ursa, Roku, Azula, showcase a tragic/Shakespearean family that is full of conflicting ideals. What I also like so much about Fire is how much insight we get into Fire Nation culture in its schools, military, celebrations, and general living. In addition, I enjoy Zuko's episodes with the original cast - all of them are engaging and fully develop both Zuko and the character he is with. Lastly, some of the best action set pieces take place here.
ATLA and worldly themes:
Redemption: Redemption is a huge theme throughout ATLA as most of the characters are trying to right past wrongs or improve on the sins of their fathers in some way shape or form. Aang tries to redeem how he hid from his duties and plunged the world into chaos, Zuko tries to appeal to his father & family to instead realize how he wants to become a better person than his family, Katara tries to deal with her past and forgiving her enemies, Iroh tries to be a better guide for Zuko than he ever was, while Toph tries to cope with her upbringing.
Buddhism/Taoism/Hinduism and enlightenment: Much of the concepts of airbending and the avatar state deal with achieving spiritual enlightenment as there is a spiritual world, avatar state = nirvana, essence of releasing chakras and the idea that airbenders are defensive only. While it is not overt, there many undertones throughout the show of these religions and how they work to the show as a whole. Along with this, the whole idea of the spirit world is a sense of religion as well.
To Kill or Not to Kill: There are several scenes in the series of characters who have a lot of conflict with killing people: Jet, Zuko, Katara, Aang and so on. Aang has a high degree of difficulty deciding whether he should kill such an evil fire lord(there's even an episode dedicated to it). Katara uses forgiveness when she knows she can kill the man who killed her mother, Zuko has to learn what he really wants to do with the avatar, his family and others, Jet has conflicts in how he wants to deal with firebenders. As such, it's a lot of debate about whether or not killing is the right way to handle certain situations which is quite a feat for a kids' show.
Clashing Cultures: I love the amount of distinct detail given to every elemental and even subculture (Kyoshi, swamp & sandbenders). In theory, this is true of how people are; however, I think it makes the comparisons of each of the four elements and their cultures a whole lot more fun in universe. For example: The Fire Nation is considered evil, uses Shaolin Kung Fu, and has red/points throughout their universe. The Air Nation is nearly gone and has only peaceful monk temples & fashion, uses Bagua, and has an overwhelming sense of peace. The Water Nation seems to be modeled after eskimos, uses tai chi and has many "good guy traits." The Earth Nation seems to have a clothing from a specific Ancient Chinese dynasty use Hua Gua fighting and offer a vast array of both good & bad people leading to the concept of a more neutral mindset. As such, it's fun to see how these come into contrast in LOK and how they work to show stereotypes.
As I feel this is long, I will place the rest of these ideas from LOK in a Part 3.