Not essential to watch the first one as it does not age well with time.
Road Warrior is a must watch and it's the genre defining movie.
The 3rd one only good for one half of the movie which you can skip unless you want to hear the theme song.

The idea of mad max is like a mythical figure. All these movies are just moments of his life and it's not heavily interconnect with each other in the sense of first movie leading to the second one. You can watch it as standalone.

M I N D B L O W N....
It's not the deepest story you'll ever watch, but the vehicular mayhem basically showing the middle finger to the furious franchise. It does not need to break physics to deliver edge of the seat action. Best of all it's not the CGI videogame crap. The villain has lesser development screen time than Ultron and yet his menacing presence fully felt throughout the movie. Guess you need a 70 year old film director to show how it's done.
Don't let this be Edge of tomorrow of last year.

The other really admiring qualities of the movie is how they manage to establish action sequences geographically. No matter how quick were the edits,you are fully aware what is going on and can follow the flow of the crazy action without losing track.

Dang! Just found out we missed out some milk maiden story bits about the war boys. They could be the ladies who release the waterfall near the end of the movie.

In regardless of that...everyone please still go watch it. We just don't get movies made like this anymore.

As much as giving all the love to George Miller, it's worth noting the studio did stand behind the problematic production and topping up budget as things got behind schedule many times over. They insist to reshoot second half of the movie after seeing the first 42 mins because of how much they believe in it.
Let's hope the movie will have legs to see through fast tracking of sequel/s. Mad Furiosa's script already brewing according to some of the candid interview.

To those who wants a little backstory, do give this a try.

It fills the blank of the two lieutenants of Immortan Joe and the origins of Nux. It shows a little bit of the milk maidens and the reason for the wives. It's not overly preachy and long winded. Pretty good read. The next one is about Furiosa and I believed these comics are from George Miller's production notes.