Gundam Unicron is a Universal Century show, aka the main Gundam timeline. Earth-1, Marvel 626, what have you. The one with the space Nazi's and the space psychics. Here's what you need to know before Unicron.
MOBILE SUIT GUNDAM
Mobile Suit Gundam, AKA Gundam 0079-The One Year War. Earth Federation versus Space Nazis. The Space Nazis started off as a legitimate movement towards independence from the Earth but the head of the space Nazis, the Zabi's, killed the peaceful revolutionary, the Zeon guy and usurped his movement. The Space Nazi's live in colonies and mobile suits were used to construct them, so they had a tech advantage when the war started because they were using these things and the Feddies were using battleships and space shuttle like things. Radar doesn't work in the MSG universe because of some particle their nuclear engines create so that's why hand to hand and big robot guns are used instead of everything being drones and missiles. Anyways the plot overview. Kid's dad makes Feddie Mobile Suit on colony, called a Gundam. Colony gets attacked to stop this new weapon from rolling out, kid jumps in suit and joins a ship of newbies and fight in most of the major conflicts of this One Year War. Char, the guy in the mask, hates the space nazis more than anyone because they killed his dad and drove him and his sister into hiding, He's the rightful Zeon heir. So he pretends to work for the Zabis and kills them all, including one of his friends, in hilarious fashion while wearing a mask. He meets the Gundam kid a lot and they fight. There's a love triangle between these two and this lady who gets killed. Oh they're also both have an enhanced form of spatial awareness that makes them excellent pilots, with limited telepathic and precognition. Called Newtypes. Zeon's theory was that as people grew up in space they'd evolve to adapt to the harsh conditions "be free from earth's gravity" and eventually come to a peaceful understanding without war. The series ends with the Nazi's losing, Char escaping, and the Gundam boy getting a cushy teaching job on earth while having his career torpedoed because of fear that he is one of these newtypes and a danger to the Federation government.
GUNDAM 0083: STARDUST MEMORY
No, not a Jojo part. Also while the next important event chronologically this is nowhere near the next show produced. It's a retcon/presequel to a very important event to set up the actual sequel to MSG. Basically it's Metal Gear in Space. The Space Nazi remnant steals a nuclear equipped walking death mobile and a test pilot who was in the non nuclear suit at the time of the heist spends a few weeks chasing him down. The space nazi's do in fact nuke half of the Federation fleet and drop a colony on the earth (something that also happened before the start of MSG) and the Federation pilot eventually wins, sorta. This action causes the Federation to form a taskgroup called the Titans to really crack down on the Space Nazi's who remain...and they get swanky Black and red uniforms...
ZETA GUNDAM
The one where everyone dies and no one gets a happy ending. Guess what, the Titans are tyrannical assholes who oppress all of the people in space, including gassing millions of peaceful protestors and other heinous shit. Another Gundam Boy shows up, gets punched a lot, steals a Titan Gundam his parents designed, and joins the AEUG, the Anti Earth Union Group, a lunar formed group to counter the Titans. It's like Star Wars, Rebels versus Empire, only with more death. Among the crew of the Argama, the ship that the Gundam Boy defects to, is this guy named Quattro Bagina who happens to look a hell of a lot like Char. Because he is Char and decided that Four Vaginas was the perfect cover name. He's upgraded from custom red mobile suits to custom GOLD mobile suits and is fighting for the good guys. The previous Gundam boy also joins up briefly and they calmy and rationally squash their beef over the love triangle thing where their lady love may have been shot and killed by one of them. Neo Space Nazis show up later on and join the AEUG to beat the Titans. Pretty much everyone dies in the last few episodes and the main character is left in a vegetative state by a powerful telepathic backlash.
ZZ GUNDAM
Hey let's follow up all that death with a light hearted comedy take on this universe that starts IMMEDIATELY after the end of Zeta Gundam. The Titans were defeated but the AEUG is down to one ship, with one bad pilot, and two suits that can still go. Char is gone and the dominant power is space is, once again, ze space nazis. So the AEUG goes to this junkyard colony and picks up a bunch of brats who may or may not be pretty okay pilots and newtypes that kept trying to jack their stuff and sell it for scrap. Oh, the main character is voiced by the guy who does Franky in One Piece and steals every scene he is in. Anyways the space nazis kidnap his little sister and he keeps doing wacky stuff to get her back. The bad guys are bumbling for the first half until the show remembers it is a UC Gundam show and people start dying left and right in the second half. The bad guy is the original "Char Clone", ironic because he's probably a Zabi clone who also starts a civil war among the Space Nazis. He has a vat of naked little girl clones who keep ending up joining the good guys. This little girl is also basically the prototype of every loli/yandere character ever. Anyways a lot of people die, the good guys win, the AEUG becomes the regular Federation forces.
CHAR'S COUNTERATTACK
Hey remember how Char was a good guy in Zeta? Totally over domination? Squashed that beef with the Original Gundam Boy over their mutual lady love? Given up the rapid migration to space plan his father valued so much? Yeah, fuck that, walk it all back. Neo Neo Space Nazis come riding back in on their awesome asteroid fortress, which is gonna get dropped on earth. They fight a lot and they both die kinda sorta trying to stop the asteroid from hitting earth.