Is there any particular reasoning behind the Watch’s horn blast System (1 for Rangers, 2 for Wildlings, 3 for Others)?

Rule of Three.

As for why that order…it’s about dramatic tension. The sudden spike in tension that comes from going from one blast meaning “friends” to two blasts meaning “enemies” doesn’t work if it goes one = wildlings and two = rangers. 

Likewise, the two/three structure allows for a further spike in tension: you thought you were dealing with a regular enemy, but now you’re dealing with a much more dangerous threat!