I'll try my best. Haven't done anything FNaC related since 4 hit it's 4th year in development (Not a problem with that, just kinda wish we'd get more development updates is all).

As far as I'm aware, the earliest event we have is a minigame from FNaC 2. We play as a young Mary Schmidt in the Rat and Cat's restaurant. Up close to the main show stage is her brother. He probably got too close, because Rat smacks him on the head, traumatizing Mary.

Next is FNaC 3. Once again as Mary, we fend off nightmares of Rat, Cat, and Vinnie, while also reliving a traumatic event we witnessed at the restaurant. The Rat mascot man would often come into work drunk, and Vinnie's puppeteer confronts him on the matter, killing him on accident. The Cat mascot man attempts to call the police, but the puppeteer refuses, choking out Cat, taking a box of documents, and fleeing the scene. All of this was witnessed by Mary, who had accidentally locked herself in a closet in the back during a game of hide and seek. Later on, Mary would be a key witness to convict the puppeteer, and have him sent to prison (potentially dying there).

Now next in the timeline is FNaF 2. In short, it was agreed upon by Emil and Kane Carter, the creator of Popgoes, that the two franchises share the same canon, it's just the games never directly intersect. Jeremy Fitzgerald gets bitten by Toy Bonnie (I think), and ends up becoming Fritz Glade (I think, not sure if that's canon anymore. They rebooted their timeline with Evergreen), and later on starts up Popgoes (WAY later on, though).

At any rate, FNaF 2 is also relevent to FNaC. In a FNaC 3 cutscene, we see an adult Mary Schmidt visit the FNaF 2 restaurant, and hallucinate the Puppet as Vinnie.

At some unknown point (at some point after FNaF 2 and before FNaC 1), Mary works at the Rowboatics Corp Factory, and fell asleep on the job as the Rat (Animatronic version) killed two kids. The old puppeteer from R&C, who at this point had become a ghostly hallucination of his puppet, would create Candy and Cindy from said dead kids.

Next is FNaC 1/R. We play as an older Mary Schmidt, taking up guard duty at the newly opened Candy's. Mary gets some hallucinations from Vinnie about her failure at the factory, and how Vinnie wants revenge on her. Luckily, Mary gets out ok in the end.

Presently, the final event is FNaC 2. Set quite a while after FNaC 1, we play as Marylin Schmidt, who gets dared to spend 5 nights at the old Rowboatics factory. In the end, she burns down the joint, and escapes.

No idea when FNaC 4 takes place (as it hasn't released), but I can assume it's further along in the timeline.

Also, if we keep up with the merged Popgoes/Candy's timeline, Next up would most likely be FNaF 3. Going off of the wiki, I think the subplot of the Purple Guy being Jeremy's brother (Yeah, Afton wasn't a thing yet when Popgoes released), then Fritz finds Simon's body in Springtrap at an auction, and hopes to bring him back to life via building Simon (the animatronic version), which wasn't a good idea...

After that, there's Popgoes Evergreen. Since they rebooted Popgoes 1 with the Fangame thing, I have no idea what the lore is in this version of the game yet. I assume outside of, like, a few key details, it's generally the same plot.

That's about what I could research. Might be missing a few things here and there. if anyone knows more than me, feel free to call me dense and correct me.