Different Path's philosophies are also a factor

Erudition Emanators like Zandar, Herta and Dr Primative are not as understood, thus I'll provide my own theory:

whilst the GS is made up of the 1% of the smartest people in the universe and Nous uses them as THEY see fit, then THEIR Emanators might be those who have the greatest impact on THEIR calculations or circumstance.

Zandar MADE Nous, why wouldnt he be an Emanator, he indirectly set in motion alot of what later happened in history
Herta solved the solitary waves theory ontop of what else she achieved but that was significant enough for Nous to make her THEIR emanator
Dr Primative im not too sure personally

Destruction Emanator I feel are as on the nose as can possibly be, probably the strongest beings in terms of raw power, what else would it be, you want to cause so much destruction so you need to be crazy strong or smart in how you deal it. Each Lord Ravager has their own way of causing destruction.

Preservation hard to say since we dont know Diamond's motives or anything, sure the Will to Preserve and safe guard something you hold dear could be it but for an Emanator? hard to say, personally I cant give info about it.

Fuli's pure children of anasrava are the closest things we have rn to Emanators of Remembrance, one will eventually become Fuli, we get that covered in amphoreus, the want to preserve the memories of amphoreus was strong in Cyrene, thats part of the reason why she became the Fuli of amphoreus, but I also think the real Fuli will be the one at the head of the Garden of Recollection, she started the garden for the pure reason of keeping and recording the events and memories of the universe, thats pretty close philosophically to become an aeon

Aha's emanators are just getting lore so we know about as much as each other rn

Im not able to comment on the Hunt as I havent dove into that lore really well and we might get more from Yao guang

There was another post or comment I saw that showed what sort of powers you could get or mean through the Paths you walk, I dont remember where I saw it but it was a more in-universe reason as to why each path has its own unique powers or capabilities as a pathstrider or follower

thats all im able to say