##Personal Opinion:
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.
##General Opinion:
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.
##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.
##Beyond the 1982 and 2011 films: