what to buy first


If I am buying from scratch and cannot afford to buy an entire system at once.  What should be purchased first?  Speakers, Amp/Pre-amp, etc??   Currently I have music with an inexpensive home theater receiver and small B&W speakers.  I have music but I will be replacing those items and putting them in another room.  
mhsmith
+1 reubent.
OP, Do you want an 'Audiophile' system? or just something to play music decently?
If the former, then I suggest trying to visit some Brick and Mortar Dealers and listening to as many speakers as you can-Then you will get an idea of what you like.
B
+1 reubent and gdnrbob.

Definitely demo as much you can, you'll save money in the long run if you know what you prefer.  Don't trust anyone's ears but your own (or maybe your wife's), but be prepared to hear more (both good and bad) as time goes on.  Once you have an ideal, it will be easier to plan it out in steps.

Speakers will be the most noticeable change, but if your receiver is underpowered they may disappoint you at home until you upgrade your amp.

Depending on your components and where you live, a power conditioner might give you an immediate improvement, or be a waste of money.

Don't overlook aspects that are not 100% about sound quality.  If you love playing vinyl, a nice turntable may give you the most enjoyment even with lesser components downstream.  Conversely if you find managing your library annoying, Tidal and a streamer might put the biggest smile on your face.

     I agree you need to answer the questions posed by timlub, mhsmith and gdnrbob above before beginning your purchases.  Once you do that, I would start with determining which speakers you want since they are arguably the biggest influence on how your system will sound and the speakers will also determine the appropriate amplification to best drive them.
     The best way to determine what speakers you want is to do what gdnrbob suggested; listen to as many speakers as you can while also identifying the type of speaker you generally like the sound of best or least - dynamic cone, planar, horn, electrostatic, etc. - so you can whittle down the abundance of choices to a smaller more manageable list of candidates. 
     Closely related to speaker selection is whether you need or want to use subwoofers in your new system.  Based on my personal experiences over the past 40 years, I consider the best approach in any room is to first get the bass performance to your preference so that the sound has a solid foundation and then progress to attaining good performance on all the frequencies above the bass. 
     Typically, it is considered more difficult, by most who have attempted it, to get good bass response in any given room than it is to get good performance on frequencies above the bass in any given room.  My knowledge has developed to the level that I've been able to attain good performance in my room for the entire audible frequency range and I believe I can assist  mhsmith and others in achieving similar results in their rooms.        
     I understand, however, that you can't currently afford to buy a complete system all at once.  If you'd like to get your new system up and running as soon as possible, you may need to deviate from  a predetermined optimum sequence of acquiring the components. I'm referring to things such as possibly delaying the purchase of your planned speakers and using your smaller B&W speakers  instead so that at least you have some speakers to use while you save for your desired ones.

Tim





onc
As many of us have found out the hard way, when it comes to hardware it is the loudspeakers that have the greatest effect. From planars to monkey coffins to open baffles there are no bigger sonic differences to be found in audio equipment. 

The funny thing is that in spite of the large sonic differences to be found, they all claim to be attempts to be accurate. It would be interesting to see whether there has been any convergence in high end loudspeaker sound in recent decades, because there are still

All you can do currently is to decide which compromise you find easiest to live with for now. For me it was a case of finding a sound I liked (clean, quick and expressive mids) and only coming to recognise much later what compromises were involved in getting that sound with that product (nothing much below 70Hz).

It will be a great help of you have a good idea of what you like est eg deep responsive bass, expressive midrange, clean detailed treble etc. You are unlikely to get all 3 at any price! Such a manmade device doesn't yet exist. So choose your compromises carefully for long term satisfaction.

Amplifier differences are far smaller at least in my experience with NAD, Marantz, Naim, Creek etc. The Naim was the one which stood out with immediacy at the price of a mild tonal washout.



Really good speakers are very expensive; I would stretch as far as I could on a preamp; Audible Illusions for example; I've had mine since they came out, and it's been trouble free. I replaced the electrolytic capacitors recently to freshen up the sparkle.

Dollar per dollar, nothing has a bigger effect than the pre-amp. The most expensive speakers in the world will give you lousy music if you don't have the right electronics.


          https://www.stereophile.com/content/audible-illusions-modulus-3a-preamplifier-page-3