What it comes down to is that the 'safe' bet is to always use the latest version of iTunes for your computer and OS when updating your device. Apple is never going to tell you anything else. It's what they design for. It's what they test for.
That leaves you with word of mouth sources and your own judgement when it comes to older versions of iTunes. They may work. They may not. Or worse, they may be unpredictable and work for some and totally mess up for others. Given that even the right iTunes version can occasionally run into issues, if the update fails then you'll never know whether it was the version, or just bad luck that caused the problem.
Or you could just use the OTA update method. It's a bit riskier, but it seems to work well enough for most people. At least on newer iPads. And you can always go back to the computer and re-install if it doesn't. I used the OTA on my iPad Air. It took about a day to settle in, and the point releases to fix all the wrinkles, but they were pretty much the same (minor) wrinkles those who updated through iTunes had to deal with.