So in what order

I'd say Him, Her, (Them). I just saw Him and Her in that order, and that made sense. I did not see Them, that seems to be more a different cut of both movies to make it into a single one, so not really part of a trilogy. So I guess you'd see Them to see how that's achieved (I probably will when it comes out.)

There are two main reasons: the beginning and the ending. I won't delve into details, I'll just say that the time frame in both the first and final scenes is later in Her, so Him gives more introduction (of both characters, unlike in Her) at the beginning, while Her gives a bit more closure at the end.

'Her' was a much deeper movie. It also had a slightly more definite ending. (Well, 'Him' kind of also leans towards that ending, the way we knew the slight wobble to the spinning top meant something at the end of Inception, but 'Her' just sort of cemented it for us.) I think it would be great to watch 'Him' first and then 'Her'. That was the order in which the films were shot as well ... Also, while I have a deep appreciation for McAvoy's performance, this was Chastain's movie through and through, and her character's way of processing with the grief is also more central to the story - given that she is the one who is 'acting out' more while his character seems to have sort of compartmentalised his misery and put a heavy padlock on it.