The lack of continuity between all four Mad Max movies, I REALLY WANT THERE TO BEA VERY ENGROSSING STORY BEHIND MAX, but it really just isn't there. The world is great and so are all the characters, but there's no really timeline or map. I guess in some sense that's what helps create the feeling, but I just want there to be MORE to fanboy over.
The continuity between the first Mad Max (the one that has a
sort of recognisable civilisation, albeit gone rotten after an unspecified global disaster) and the second (the one where either civilisation has gotten somewhat worse or he's moved even
further away from the last vestiges of law and order) is pretty much all there if you want to see it. There's been a tipping-point and Max is forced to tip over with it, losing his anchors to the old 'real world' (his family) along the way.
Around my way, #2 (The Road Warrior) is
the Max Max film, if you don't specify the numeric or subtitle element, of course, and it
can be viewed as self-contained. Things are terribly, terribly wrong (at least in this particular part of the world, but then one must assume all over the place; at least enough so that nobody cares about the automotive carnage going on in these wastes) and you've got people trying to drag the world up, others trying to drag it down and this guy who is not so altruistic as the former, but he's certainly not so nihilistic as the latter. If you'd never seen #1, where he was an actual highway patrol officer who lost everything he loved, you might wonder as to why, but it doesn't hurt or hinder things.
#3 (Thunderdome) sort of carries on, in a 'not as good a sequel' way. It's no Highlander 2 (a.k.a. the one they
completely ignore when developing Highlander 3, the TV series, etc) but it always seemed to be a sequel-for-sequel's sake, to me, in the typical '80s manner of jumping on (if not downright jump-starting) a bandwagon. But it still, at its core, has the same mentality. There's attempts at civilisation (separate from the Petroleum People's efforts, presumably successful if the end-narration of #2 is to be believed) at Bartertown, and the Oasis kids and at least one other 'unaligned good-to-neutral party' (the gyrocaptain, and his kid) surviving, and if it weren't for politics and other practicalities it's quite possible that Bartertown would be a virtual nirvana, compared to what's around.
#4 (Fury Road), just released, certainly
is disjointed to canon, but then you can probably argue where it differs it's more a reboot than direct sequel to its 30yo predecessor.
We know from #
3's closing narration that the Oasis Kids made themselves a colony, too, certainly lasting beyond the timeline for #4, and presumably whatever happened to Bartertown, Max hasn't stuck around in the same area because despite Auntie's eventual mercy he's probably not very welcome. So it's not surprising he finds himself in a
new dystopian territory where there's been a fusion between the ethics and cult-of-personality of the Humungous gang from #2 with the principles of establishing a (now multi-noded) barter society from #3. (It seems perfectly attuned to the creation of a trade and combat and exploration computer game, with a massive 'sandbox' environment to roam around in. Reminds me a lot of the web-game Minethings and the flash-game Caravaneer and could probably use a GTA3-like game-engine on ... or GTA4, but I'm a bit out of date with that game series.)
Anyway, for the engrossing story behind Max, look no further than film #1. Then take the 2015 maybe-reboot with a small pinch of salt. Although I do like a number of the touches to it (underspeed camera/overspeed projection thing) that links it with the original(s), there's a lot of "awesome but impractical" to the whole local geopolitical system it depicts, as I recall. Still, as almost pure petrolpunk-porn, I'd say it works.