Arise, the movies, the manga, and GITS:SAC are all different universes (Shirow himself has said this).
I'd watch it the two movies (avoid the CGI-ed remake of the first one), then all of three seasons of SAC[1], and then Arise: AA.
And for those who don't know, AA is the series based off the four episode OVA. The OVA... sucks, the pacing is really bad, and they basically quit making more of it so they could make a proper series out of it. It isn't bad, but it's no SAC; it's more like an animated version of the manga, but not as Shirowy.
Just realize you're watching three different almost unrelated works.
[1]: Did you know SSS was meant to be an entire third season? They couldn't secure the budget for it, so they made a compressed movie like they did for SAC and 2nd Gig (The Laughing Man, and The Individual Eleven, respectively).
Yes, that's why I said that they aren't all in the same universe.
I feel Arise should come first because it has the most "origin story", and I put SAC last, because I like to keep the best for last.
And, like I said, it "feels" more chronological that way (to me). TBF, it's been a while since I saw SAC and the movies, so it's possible I misremembered.
Regardless of "origin story", I'd argue for the (non-CGI'd) original film to be viewed first. The reason is that it contains all the essential themes, visual motifs, and characters. To me it still feels like the "core" of the films/shows.
Perhaps.... but I am skeptical. The original will always have a special place in my heart, but it feels like there's too much gratuitous nudity and violence that almost masks the deeper interesting sci-fi part. Bateau and the Major seem really well developed, but the other characters feel two dimensional (e.g. Togusa and the Old Man). The later movies never really spoke to me, but I'll have to re-watch them.
SAC really seemed to nail the character portrayals, IMO, and felt more accessible. Arise adds the backstory of how they got together that I really had always wanted to see.
Maybe a season of SAC, then the movie(s), then Arise? I don't know, I'm sure the order is not critical. It's not like Star Wars or Star Trek movies in that regard. :)
One thing I really liked in Arise is that they showed how Togusa joined the Major's team (and how they joined Section 9). We got some good back story on Togusa in Ghost Tears.
Unfortunately, Alternative Architecture (and the Arise OVAs) are all behind Funimation's subscriber paywall. I've seen the first three Arise OVAs on Netflix (although OVAs 1 and 2 come down today). The fourth OVA hasn't come to Netflix (at least here in Canada).
And, beware the "2.0 edition" of the original movie that replaces several iconic scenes with crappy CG re-renders. It's inexplicable that someone thought that was a good idea.
Arise (parts 1, 2, and 3) are on Netflix. I had to use Wikipedia to tell which order they were in, until I read the descriptions more closely. This is a prequel, of how the characters came together.
Stand Alone Complex is on DVD. I like it a LOT more than the movies, as it really portrays more characters as 3-dimensional than just the Major and her partner, Bateau. I don't know if it's on Amazon Video, but there's a decent chance of it.
I agree with DiabloD3. Tobold's recommendation is not a good viewing order. These works aren't set in the same continuity, so it doesn't make sense to order them in a way that feels chronological.
Here's my preferred order, along with some info/opinions about each work:
• Ghost in the Shell (1995). If you watch one thing in this list, watch this. Make sure it's not 2.0, which adds lots of ugly brown CG to the 1995 version.
• Ghost in the Shell 2: Innocence (2004). This is set several years after the events of the first movie. If you're pressed for time, you can skip this without missing anything important in other works. Honestly, Innocence is my least favorite work in the franchise. My biggest criticism is the ponderous pacing. Mamoru Oshii likes to dwell too much for my tastes.
• Stand Alone Complex (2002). While the characters and technologies are similar to the movie, this is a completely different universe. It also differs from the movies in its treatment of philosophy. Instead of having characters say something like, "What does it mean to be human?", the show tends to set up circumstances that make you, the viewer, ponder such things. It's much more natural.
• Stand Alone Complex: 2nd Gig (2004). This continues the story from Stand Alone Complex. If you haven't watched the first season, you will be confused.
• Stand Alone Complex: Solid State Society (2006). This movie is set several years after the events of 2nd Gig. Again, if you don't watch the earlier seasons, you'll be confused.
• Ghost in the Shell: Arise (2013). This is a continuity separate from both the original movie and Stand Alone Complex. You don't need to watch the earlier works to enjoy this series, but you'll miss some shout-outs and references. More importantly, watching Arise first will warp your perception of the earlier works. It would be like deliberately watching Neil deGrasse Tyson's Cosmos before Carl Sagan's.
• Ghost in the Shell: The New Movie (2015). This is set after the events of Arise. You'll definitely be confused if you don't watch Arise before this.
Except for Innocence, this is the same order in which these works were released.
If you're looking to stream these, you're going to have a bad time. While they're mostly available on Amazon Video, the quality is lacking. Some only have english audio. Some are mislabelled. Some are "special" editions with various edits, altered artwork, and "updated" effects. If you want to make sure you're getting the ideal experience, your only hope is to blow money on the DVDs or Blu-rays, or pirate them. :(
Hulu has a few of these. Maybe not the "ideal" versions though. Definitely has the dub of SAC. High def version of GITS 25th anniversary edition. Has some version of Solid State Society, Ghost in The Shell 2.0, GITS: Individual Eleven, and GITS: Laughing Man.
* Ghost in the Shell: Arise - Alternative Architecture
* Ghost in the Shell: The New Movie [sic]
* Ghost in the Shell
* Ghost in the Shell 2: Innocence
* Ghost in the Shell: Stand Alone Complex
* Ghost in the Shell: Stand Alone Complex 2nd Gig
* Ghost in the Shell: Stand Alone Complex - Solid State Society
Not all of them are strictly speaking in the same universe, but afair this gives the most chronological feeling results ;)