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 (2011) doesn't introduce any information that is necessary to understand the earlier film.
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.
More importantly than any of this, the simple fact is that most fans of The Thing (1982) would probably argue that you don't really need to see the prequel, 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.
As it happens, Carpenter agrees with me on this point. I'll try to dig up the quote, but if I'm not mistaken, he said that he considers the comic book series by Dark Horse Comics to be the only potentially canonical addition to his film's universe, and he also likes the short story by Peter Watts, The Things.