The Zenith expansion provides most of the goodies, extra ships, and a lot of the tools you will need to go after the other expansions. I'm not sure how I would play without this expansion, as I utilize everything in it every single game I play.
The CoN expansion, from my perspective, is for advanced players in an already advanced game. It has some of the most unforgiving AI in the game, and hybrids alone are worth the price of admission, but in my own opinion I feel that the ships and the hybrid material are best utilized by players that know what they are doing. I just recruited a friend of mine into buying all the expansions, but, we are not playing with a lot of the really difficult stuff because it requires more experience.
The fallen spire expansion is amazing, and the campaign always feels fresh and exciting. However, I think this is best for players that have already tortured the AI and are playing on high difficulties and need something else to challenge them. It is more difficult to have much success against the campaign without the Zenith expansion. I don't see how someone would conquer a lot of these events without a great deal of understanding on the mechanics from prior expansions.
So, in order of my favorites, Zenith->Spire->CoN . I have enjoyed them all so just pick them all up.