What order were the Xenoblade Chronicles games designed to be played in?

• All three games are completely separate stories and games that happen to share some similarities in terms of races and items and so on. The series is very similar to Final Fantasy in that regard. Without going into spoiler territory, the games do sometimes reference each other, but not in any significant way. You can play the games in any order or not at all.
• XC2 and its DLC were written such that you'd play the main game first, as the Torna DLC wasn't even available until a few days ago. Playing the DLC second is recommended.

Without spoiling anything, Xenoblade Chronicles ties into Xenoblade Chronicles 2.

Spoiler:

At the end of Xenoblade Chronicles 2, it is revealed that when Klaus activated his device, he split the timeline of the world into 2 halves. One half is Xenoblade Chronicles 1, the other is Xenoblade Chronicles 2. You can hear dialogue from the end of Xenoblade 1 as you approach the final boss in 2.

However, this is only a reference, so the only thing you'll be missing out on by playing Xenoblade 2 first is a full understanding of the reference.