What a great request! I'm the current Story Lead for the game. TBH, it wouldn't be a bad idea for us to do something like this in general for everyone sometime. But since you asked, I'll try to summarize the important bits.
For the record ... when you're looking at the Archives, you'll notice that they are organized by release. Each release has a printed fiction that comes with the set, a series of shorter pieces used to preview upcoming cards, and a longer web fiction. We try to keep the bulk of the story meat in the longer pieces (rulebook and longer web pieces), so if you're looking to prioritize your reading, those are the places to start. The shorter ones are great too ... they just aren't as central to the story as the longer ones are.
Alright ... here we go.
As Gomorra was trying to get back on its feet after The Storm under the protection of Sheriff Dave Montreal, an outsider named Rafi Hamid came and orchestrated a mayoral race in an attempt to bring democracy to the filthy masses of the frontier. The local outlaw gang, led by Sloane, was hired to put a stop to it and they did, by murdering the two candidates in broad daylight ... an event that has been dubbed the Election Day Slaughter. In their desperation to fill the office, the town signed a deal with the devil, swearing in Nicodemus Whateley, a powerful warlock from Gomorra's past.
During the Slaughter, one of Sloane's own, Lawrence Blackwood, felt the need to purge his guilty conscience, leading to his arrest and execution. This event enraged Sloane so much that she led her gang into town looking for revenge, but found a nightmarish scene as a swarm of tumblebleeds attacked the town. She should have cut her losses and retreated, but a mysterious inner voice spurred her on until she found Dave Montreal and shot him dead. In his absence, Abram Grothe, a preacher turned deputy/sword-wielding hero of the people, has stepped into the vacant office.
Meanwhile, Gomorra has been suffering from an outbreak of sickness. While the town's minds and healers have been struggling to stem that tide, the Fourth Ring circus, led by Ivor Hawley has stepped in to help, offering some of their tents to help the sickest among them.
But he clearly has a secret agenda. Not only has he been directly responsible for one murder in the town, but he's been gathering powerful relics for an unknown collector as well.
The Morgan Cattle Company has had their share of trials and triumphs. An alleged heir to Nathaniel Morgan's cattle empire has appeared, and her name is Lula. She's spoiled, entitled as all get out, and willing to do whatever it takes to get rid of Nathaniel's wife, Lillian, and claim the whole thing for herself. At the same time, the brilliant minds of the Morgan Research Institute, headed by Louis Pasteur, have successfully recreated Morgan's unique breed of cattle that put them on the map during their Ghost Creek days. But not everyone is supportive of the new development; the veterinarian Kyle Wagner gave his life as they discovered the new creatures taste for meat and Max Baine refused to be a part of bringing yet another horror to Gomorra.
Hopefully, that covers most of the high points and gets you set up to follow things as the story moves forward.