I could try to give an exhaustive background on the things that take place over the course of this (so far) two and a half year run, but I honestly don't have the time for that right now. Here's some links that will give some background on the stories Hickman is drawing upon to craft his Avengers opus:
Marvel Super Heroes Secret Wars
Marvel "New Universe"
(Also, I just noticed that Dr. Zero is in that Secret Wars picture up there, which is amazingly amazing. So here's this: The Shadowline Saga)
There. That should give some background. Just don't read too far into the articles, as they do deal with events that take place in Hickman's Avengers. Oh, and there will be spoilers in this post. If you just want my read order, don't read the stuff that I write next to it.
I don't have too much to say right now, having just started the re-read. While the stories are extremely well-crafted, and the two titles play into the action and espionage genres while also retaining the "Holy Crap! It's the end of world!" types of stories that the superhero genre is so adept at, this run is still no Fantastic Four. The scope is the same, perhaps even more grand, but FF had so much heart, evoked so many feelings. The Avengers titles are plumbing the depths of morality, of law, of what it means to be heroic, but it's missing that family feeling that Fantastic Four, when well-written, has in droves. But that's okay, because the Avengers are not a family, at least not in this incarnation. They are soldiers.
I'll have more to say, I'm sure. But for now, here's a beginning of my reading order. I'll update in this post whenever I finish another stack of the story. Some bits get a bit convoluted (like should Bendis' Age of Ultron be in here somewhere, considering the time travel stuff that happens in the Original Sin crossovers?), but this is the order that seems to make sense to me.
New Avengers v.3 #1 - 3 - these issues take place before Avengers v.5 #1, as in the opening pages of that issue, Captain America has a dream/memory of events that take place in NA #3. Also, he is wearing the old-style costume that he eschews at the end of v.5 #1.
Avengers v.5 #1 - 6 - the first three issues are the story of the garden on Mars, and introduce Abyss, Ex Nihilo, and Aleph, all of whom become major players later in the series. Following these three issues are stand-alone "origin" issues, sort of, featuring Hyperion, Smasher, and Captain Universe. A good idea, these three, as they are the characters with whom even long-time Marvel readers might be the least familiar. On a personal note, putting Hyperion on the team is awesome, since he's basically Superman, and has now not only been displaced from his own planet, but from his own universe. And Smasher is Dan Dare's granddaughter.
New Avengers v.3 #4 - 6 - a brief storyline that pushes the Illuminati into the place they thought they could avoid, and much sooner than they expected. We also see the beginnings here of a group that is currently playing a major role in the Avengers titles, The Cabal. What New Avengers does really well is to show these extraordinary beings engaged in conflicts the size of which mere mortals would have trouble even conceiving. The heroes of the DC Universe are very often put into universe-altering conflicts, but the Marvel heroes are not often let loose on that scale. Yes, there's the occasional intergalactic war or something, but only very rarely do we see the nature of their very reality being threatened. It is cool to see Marvel heroes interacting on the god level of their universe.
Avengers v.5 #7 - 9 - A WHITE EVENT!!! I thought I was the only one who enjoyed Marvel's failed first try at a "more realistic" universe, the "New Universe." But here's Hickman re-introducing elements and making them frickin' awesome. The introduction of Nightmask and Starbrand here have vast consequences, and Starbrand's origin in particular really does play into the ramifications of the superheroic on the mundane. Also shades of Civil War here. The end of this story does present a continuity problem, as Starbrand and Nightmask are relegated to the Dyson sphere that Iron Man is constructing, the existence of which was previously only known to Stark, Reed Richards, and Hank McCoy. Does this mean that the newly-brain wiped Captain America knows of the sphere, or just that he trust Stark enough to allow him to sequester these two superbeings without knowing where they are? That doesn't seem like Cap to me.
So that's it for now. I'll update as I go, and as I figure out the storylines. Any suggestions for ancillary reading, or for changes to the order are more than welcome.