order of improving sound quality in system?

The choice is too system dependant. Any component could be the weakest link. Cables can be the difference between good sound and "magic", so they are important too.

I say buy the best speakers you can and work from there. Amp and pre-amp choices will synergized with the speakers. Source components improve most any amp/speaker combo. Use cabling to fine tune your system. Change the speakers and you may need to start all over except for source gear.

You won't get anything in the way of a clear answer to you question...if you do a search you will find this has come up many times...you may even find someone starting with a power cord...HeHe

I start by listening to speaker systems, some people buy over the web based on research and opinions without first listening...I don't. Once I find a pair of speakers that I'm sure I will be able to setup properly so as to maximize their full potential...I begin to ponder components...amps next.

Choices here are vast and by now I'm able to shrink my choices down to several thousand...after all, speaker choice will dictate amp choices...and of course the room comes into play again...ie, i'll need to reach fairly high SPL's at times.

Next I move on to the preamp...of course I now know my amp choice which dictates types of preamp I'll research...passive designs could shine with the right amp so those may also be on the table...along with solid state and tubes...again, lots to ponder and this is the point were neutral could give way to flavor...my ear, my choice...there is no right or wrong direction here...this is about fun and enjoyment.

Last...Source, just as important as everything else in truth but I usually have and like several...constant state of flux for me so I would never start here...technology moves fast in this area.

Cables: laster than last.

And of course room treatments for those that can at the end.

IMHO,
Dave

thanks a lot everyone!

Speakers are the most colored component in the system. Different brands/topologies sound very different, so you first need to find a pair that you like. Nothing you put upstream from your speakers will make you happy unless you have a pair of speakers that suit your tastes.

The requirements of the speakers you choose will then determine what type of amplifier you need. For instance, if you like power hungry speakers like Magnepans then you have to get a powerful amp. On the other hand if high efficiency horns are more to your liking then you need a low power SET.

There is no way of getting around this fundamental principle of building a system so the speakers must come first. You can then choose components that complement the speaker and amplifier.

Source, preamp, amp, speakers, wires. You need to "get it right" from the beginning, nothing downstream will make it any better.