One of my favorite films that is not often considered a "mafia movie" is RocknRolla. It's a fantastic movie heavily featuring British and Russian mafia, but that may not make it a mafia movie.

I absolutely recommend reading The Godfather, the book upon which the movie is based.  I liked it a lot better than the movie, but I also read it first.  I also think one should watch Casino and the Goodfellas.  For mafia media that's newer for sure The Sopranos.  I also recommend reading up on actual mafiosis, I had a great book but I can't remember the title.  You can look a lot of them up on Wikipedia. 

I haven't really dived into these sorts of materials, past The Godfather. Granted, it offered a few nice weeks of exciting inspiration for acting on here but now it's mostly faded into the background for me

I particularly liked the Irishman but there are other good ones

One series I tend to keep going back to is Inside the American Mob. It is a documentary series from National Geographic. If I remember correctly it came out in 2013. It has some good information, some surveillance footage and interviews with members, associates, and law enforcement agents. It’s got Phil Leonetti from the Philly Crime Family, Michael Franzese from the Columbia Family, and Joe Pistone. There’s also an interview with Selwyn Raab who was a crime reporter in the 70’s and 80’s. On the topic of Raab, he also wrong a book called The a Five Families that is incredibly insightful. 

Not precisely Mafia as much as crime, the Ghost of Eden Park is a great non-fiction book that explored one of the biggest bootlegging operations by George Remus during the Prohibition era trafficking whiskey and the cat and mouse game of someone at the Department of Justice as well as the bootlegger's own weird and messed up relationship with his wife.  Not sure if I'd classify it as essential, but definitely material that colored in the era for me that we're all playing in currently. 

There are so many good books out there, both real life and fiction based on real life that it's hard to choose one.

I enjoyed 'Five families' by Selwyn Raab very much and would recommend it.

Reading the original Godfather by Mario Puzo (a singer in the book is believed to be based on a young Frank Sinatra) is also worth reading, even if you've seen the film

Similarly there are documentaries on the Naples mafia which are absolutely amazing.

Yeah, Goodfellas was my favorite. The Godfather was ok, I just found it a little slow. Bronx tale was also one I really enjoyed.