UC Gundam does a great job of balancing character drama and politics imho.
Char vs Amuro is the best.
Because I REALLY love talking about Gundam, ehre is a primer for you guys. Don't worry, I haven't included spoilers for Unicorn. I'll write it in timeline form. There will be spoilers for 0079, 0083, Zeta, ZZ Gundam and Char's Counterattack though.
Universal Century begins once the Earth Federation begins making plans to colonize space. No concrete date has ever been given as to when UC0001 matches up to AD, but I've heard some people suggest 2040. Doesn't really matter.
UC0050s. A man by named Zeon Deikun becomes a popular philosopher and politician. He teaches that the Earth is sacred and needs to be protected. More importantly, he teaches that by moving to Outer Space, humanity will continue its evolution, becoming a New Type of man. Newtypes are said to better adapted to the vast emptiness of Space. They have enhanced enhanced spatial awareness and can communicate telepathically, amongst other things. Eventually Zeon Deikun becomes the leader of the cluster of colonies on the Far Side of the Moon called Side 3. Also, he is a staunch advocate for independence for Spacenoids (the franchises' term for space colonies). He's very popular. He has two kids, Artesia and Casval.
UC0068. Zeon Deikun dies of a heart attack. The circumstances of his death are mysterious. Some believe that Zeon Deikun's trusted friend, Degwin Zabi, had him poisoned. It's certainly possible that that is the case, but the franchise never says for sure. What is known for sure is that Degwin Zabi takes advantage of the power vacuum and becomes the leader of Side 3. Artesia and Casval are spirited out of Side 3 for their protection and assume aliases. Artesia becomes Sayla Mass, Casval eventually assumes the name Char Aznable. Believing the rumors of his father's assassination, he launches a plan to get revenge on the Zabi family.
UC0070s. Tensions sore between the Earth Federation and Side 3. Both sides build up their militaries. Side 3 begins developing weaponized versions of their "mobile workers" construction robots. They eventually become Mobile Suits.
January UC 0079. Side 3 declares itself the Principality of Zeon and launches an attack on the Earth Federation in the name of independence. This War is called the One Year War Initial fighting lasts for two weeks and half of the human population is killed due to the tactics that are employed. Nuclear weapons and chemical weapons are used indiscriminately at this time. Most horrifically, the Principality of Zeon drops a space colony on earth. They were aiming for the Earth Federation's military headquarters in Brazil, but miss. Instead it hits (and destroys) Sydney Australia. Afterwards, both sides come together to agree to terms of warfare. Weapons of mass destruction are prohibited (including colony drops). This treaty is called the Antarctic treaty. During this time, mobile suits make their debut in war. Casval Deikun, under the alias of Char Aznable by this time has infilitrated the Zeon military and has gained renown from his performance a battle called the Battle of Loum (in which the Earth Federation Space Force (EFSF) is thoroughly crushed). He likes to pilot customized version of the Zeon main mobile suit, the Zaku II.
Following the Antarctic Treaty, the war settles into a 7 month long stalemate. Zeon manages to take vast stretches of land on Earth (in order to make up for their own lack of natural resources), but they can't drive home the win. Meanwhile, the Earth Federation continues to play catch up to Zeon's mobile suits. They develop the Gundam.
July 0079. Just as the Gundam is completed, Char discovers the colony it is being constructed. While his unit is attacking the colony, a civillian named Amuro Ray finds his way into the cockpit. Even though he's a novice, due to the machine's capabilities he is able to stand toe to toe.. The survivors of the colony climb on board a EFSF battleship called White Base and evacuate the colony. From that point on, they are roped into fighting for the Federation as they protect their prototype mobile suit.
Through the rest of the war, the Federation is able to push back Zeon into space. Char begins executing his plan to get revenge. The youngest son, Garma, is betrayed by Char and led to his death. the second youngest son, Dozzle, is killed by Amuro. Degwin Zabi is betrayed by his oldest son Gihren, and Gihren is killed by his sister Kycillia. Kycillia is killed by Char. Only one member of the family survives. Dozzle's infant daughter Mineva.
Towards the end of the war Amuro encounters Char's protege, Lalah Sune. She is a gifted Newtype. Amuro and her quickly bond, though she is a Zeon pilot. During a battle with Char, she is killed by Amuro. Both men blame each other for her death.
After the war, most of the remnants of Zeon flee to an asteroid called Axis in the Asteroid Belt, including Char and the baby Mineva Zabi. Side 3 is made into a puppet colony called The Republic of Zeon.
UC0083: A nuclear armed Gundam is stolen from an Earth Federation Base near Torington, Australia. The Gundam is stolen by Gihren Zabi loyalists, who use the nuke to attack the Earth Federation Space Fleet. Afterwards a colony is dropped on North America. In response, the Earth Federation creates a elite task force to crack down on Zeon remnants. This force is called the Titans.
The Titans are harsh in performing their duties. They brutalize and bully spacenoids. They are an elitest faction
UC0087: In response to a colony being gassed by the Titans, a...terrorist?... group called the AEUG (Anti Earth Union Group) is formed. Char assumes the identity of Quattro Bajeena and quickly earns a high rank in the force. Eventually Amuro, who had been under house arrest after the One Year War, also fights against the Titans, but for an Earth-based anti-Titans faction called Karaba. a young Newtype named Kamille Bidan also joins, as does the captain of White Base from the One Year War, Bright Noa. Towards the end of the conflict, Char reveals himself to the world as the heir to Zeon Deikun During this time, it is revealed that the Federation had been doing experiments on people to invoke Newtype-like abilities. These people are called Cyber-Newtypes
The war is brutal. Eventually Zeon Remnants from Axis arrive and the war (later called the Gryps conflict) becomes a 3 way war. The final battle takes place near a colony that had been retrofitted into a laser. The AEUG manages to take control of the laser and uses it to destroy most of the Titans fleet. However, in the course of the battle the AEUG loses many of its members. Kamille ends up in a coma. Char goes missing
UC0088: Axis Zeon begins an invasion of Earth. They want possession of Side 3. It's leader, Haman Karn, is the retainer of Mineva Zabi and uses the young girl as a puppet. Eventually the AEUG manages to find a replacement crew and fight back. A rift develops between Haman Karn and supporters of a boy named Glemy Toto, who may be the illegitimate son of Gihren Zabi. Glemy had a secret Newtype clone army of little girls called "Ples" (pronounced Pulls.) Both Haman and Glemy die.
0093: Char comes back! He has decided fulfill his father's legacy. Quickly gaining support, he manages to develope a military and begins dropping asteroids on Earth. HIs goal is to cause a Nuclear winter on Earth so that it will be uninhabitable. But really he wants to draw Amuro into one final duel, because he never got over Lalah. His army tries to drop Axis on Earth, but a Anti-Zeon task force called Londo Bell, which was created by former AEUG members after the Titans were disbanded, resist. Due to space magic, the meteor is repelled. But both Amuro and Char vanish during the conflict..
Also worth knowing is:
Minovsky Particles. Oftentimes you'll hear captaisn shout stuff like "Disperse minovsky particles at combat density!". This means they are dispersing a particle that jams radio communications, amongst other things. This prevents smart weapons like lock on missiles from working. Hyper charges MP are used to create beam weaponry.
Funnels: Psychic controlled weapons that take advantage of a Newtype's powers.