Which of the mangas of Arifureta is the anime based on? As far as I know, there are 3 mangas of Arifureta. 


Arifureta Shokugyō de Sekai 
Arifureta Shokugyō de Sekai Saikyō Zero, and
Arifureta Nichijō de Sekai Saikyō


Which one of them is the anime based on, and where do they fit in the animated series?
As far as I know, both the anime and the manga are adapted from the light novels. 

MyAnimeList states that the anime is an adaptation of the light novel and all the manga aside from the spin-off are just an alternative version of the light novel. Arifureta Nichijō de Sekai Saikyō is just a 4-koma spin-off detailing their daily lives so I don't think it would impact the main timeline that much. 

As for the order of events:


Arifureta Shokugyō de Sekai Saikyō Zero (as far as I know, this was not adapted by the anime as it is a prequel to the events in Arifureta Shokugyō de Sekai)
Arifureta Shokugyō de Sekai (the light novels of this are the ones adapted by the anime; the manga is just an alternative version)  
Arifureta Nichijō de Sekai Saikyō (daily life during Arifureta Shokugyō de Sekai events)