It doesn't really matter.

First of all, as you have correctly noticed, the films were made in a different order than the books (not only was Angels & Demons filmed after Da Vinci Code, they also jumped over The Lost Symbol, as explained in this related question). So this on the one hand means, the books themselves don't really build extensively onto each other (or at least not in ways significant enough for the primary story and characters) and also that the films necessarily can't rely too much on previous films without introducing connections not present in the source material.

But aside from theory, the films are indeed entirely independent from each other. They tell entirely closed and self-consistent stories each and the previous stories have absolutely no bearing on the characters or story of next films. They're not really sequels or prequels rather than just independent adventures of the same character, comparable to the majority of James Bond films. In addition to that, all the films also introduce Robert Langdon as a professor and some kind of expert for symbols as soon as he appears (although, the introduction in Inferno is a little more "abrupt"), which is pretty much all you need to know about the only recurring character to get the story started.

There are two very minor allusions to previous films (or the main character's general background):

• There is one allusion to Da Vinci Code in Angels & Demons (which thus also tells us that the former is set before the latter, contrary to the books). At the beginning of Angels & Demons, when Robert Langdon is asked for help by a Vatican policeman, he asks why they turn to him:

  Langdon: Why me?
  Vicenzo: Your expertise, your erudition. And your involvement with recent Church...shall we say "mysteries?"
  Langdon: I wasn't under the impression that episode had endeared me to the Vatican.
  Vicenzo: Oh, it didn't. But it made you...what is the word...forma...formi...
  Langdon: Formidable?

  But this allusion to "recent Church mysteries" is so faint, that it might as well be referring to anything else, since Robert Langdon seems to be repeatedly involved in Vatican intricacies due to his job (but it's highly likely it does refer to Da Vinci Code indeed). But that's pretty much the amount of connection there is between the films. And Inferno doesn't even have that (since contrary to the first two films, it doesn't really feature the Catholic church much at all).

• There is also the mystery of Robert Langdon's Mickey Mouse watch, which is shown a few times in previous films without ever giving an explanation about it, and which is only elaborated a little more in Inferno (still not going beyond one sentence, though), as also explained in this related question. But if that really counts as significant cross-movie character development is debatable.

So you can really watch them in any order that you deem fit and it doesn't change the experience or impact of the movies' stories and characters at all.