There is obviously no canonical reason to watch the movies in any particular order, but for a number of reasons, I would suggest watching them in the order in which they were released.
The Thing (1982) is universally regarded as a far superior movie than the prequel.
The Thing (2011) is a prequel, and employs a significant number of retcons.
The Thing (2011) is arguably noncanonical, because John Carpenter had nothing to do with it.
The Thing (1982) was never intended to have a prequel, but The Thing (2011) was always intended to be seen after the earlier movie. To put it another way, The Thing (1982) was never supposed to be a sequel, and The Thing (2011) was never meant to turn the earlier film into a sequel.
You don't need to know anything from The Thing (2011) to understand The Thing (1982), but the opposite may not be equally true.
Perhaps more important than any of the above, the simple fact is that most fans of The Thing (1982) would probably argue that you don't really need to see the prequel at all, whereas they would unanimously insist that you absolutely should see the earlier film. Among the fanbase, the prequel is seen as an optional addition to the real deal.
Some fans would tell you that you shouldn't watch the prequel at all, while others would suggest that the prequel is an interesting but nonessential add on to the earlier movie. A few might say that it is more or less necessary to see the prequel. Very few fans would say that the prequel is equally important and valid, and I haven't heard anyone say that the prequel is superior to the 1982 film.
In short, I would recommend that you see The Thing (1982) as soon as possible, and if you decide to watch the prequel, do so afterwards. I consider the prequel to be neither necessary nor a particularly good movie, especially as an addition to the franchise. If it were a standalone film, the prequel would be so-so, but as a Thing movie, it is regrettable.
John Carpenter's Opinion:
As it happens, Carpenter agrees with me on this point. He has been largely quiet about the prequel, but he hints that he didn't approve of the idea and has no interest in it. He said that the best "The Thing Two" story is the Dark Horse Comic book miniseries, and he also likes the short story by Peter Watts, The Things. The Dark Horse series was called The Thing From Another World (the full title of the 1951 film) in order to avoid legal conflicts with Marvel Comics related to their Fantastic Four character, The Thing.
Q. If you had made a sequel to The Thing back in the mid to late 80's, where would you have set it? In a city? Some other isolated location? Would you have even bothered had the opportunity arose for you to take up the helm and expand on the mythology? More over, what things do you think would be cool or interesting to add to the creature? Do you think adding to the list of peculiar things it could, would, and would not do would make for a more interesting alien/monster, or are you more for the mystery and leaving it ambiguous?
A. The best THE THING 2 story, I believe, was in the Dark Horse limited series comic book published in the 80's. It began with MacReady and Childs walking over the icy landscape....
- Outpost 31 Interview with John Carpenter
Beyond the 1982 and 2011 films:
Personally, I would say that a list of the relevant materials, in order of importance and potential enjoyment, would be as follows:
The Thing (1982)
Who Goes There? by John W. Campbell (the novella that started it all)
The Things by Peter Watts
The Thing From Another World comics from Dark Horse
The Thing (2011)
The Thing From Another World (1951)
This is also probably the order in which I would recommend reading/watching them.