The Thing Infection Order

Ok, for starters let's lay out every character in the movie, that being: MacReady, Garry, Childs, Windows, Blair, Dr. Copper, Bennings, Fuchs, Norris, Nauls, Palmer and Clark. Now let's get rid of people we know aren't the thing (I'm including Childs for this because he'd be at the end anyway) That narrows the people down to: Garry, Windows, Blair, Bennings, Norris, Nauls and Palmer. So, the first time we see someone assimilated is when the dog-thing enters the room with a shadow on the wall. Because of the curly hair, the shadow can only belong to three people: Windows, Norris and Palmer, and we can eliminate two of them. Windows passes the blood test so it couldn't have been him, and Palmer shares a joint with Childs, who also passes the blood test, and since he shared the joint after the shadow scene, it can only be one person: Norris. Meaning Norris is patient zero. Next is Palmer as he's the only person left to be wearing Longjohns, which Nauls finds in the kitchen trash. After him, is Bennings who we see get assimilated. Now, at this point it's safe to say Blair has been assimilated, we know it can't be before he's locked in the supply shed as he's going crazy trying to stop the thing, and before you say it, no, his pencil doesn't touch the thing, it gets close but doesn't touch it. But after MacReady returns to the suplly shed, Blair is all of the sudden fine. so he got assimilated then. Next is the blood test which reveals that Palmer was a thing, he then bits Windows' face and turns him in to a thing. Now, there is a precedent that being bitten by a thing doesn't necessarily result in you being assimilated, see Dr. Copper's blood test, but Windows was making weird gurgling noises, so it's safe to say Windows was at least partially assimilated. Then Blair attacks Garry, and I believe that Garry was assimilated, as we can see his face being stretched when Blair drags him away, which isn't something a normal face can do, but a thing face totally could. Then it's just up to interpretation on whether or not you want to include Nauls and Childs, there is a deleted scene where we see Nauls being assimilated, and if you want to say that scene is canon, go for it, and Childs is left up to interpretation, and I'll get in to him in the next part.

As it stands the assimilation timeline goes: Norris, followed by Palmer, then Bennings and Blair next is Windows and finally Garry and maybe Nauls and Childs if you see fit.