SEEKING ADVICE: Which component would you upgrade first?

GIven the enjoyment you receive from your old and new LP’s, protect them and upgrade your cartridge and turntable. With budget considerations in mind, I would then look for a newer used integrated amplifier. Finally, you can upgrade your speakers. Not the order I normally do things but in your case it might make good sense.

You do not have to spend big bucks to put together a very musically satisfying system. Sort ought your priorities sound wise, do your research. When you ask for advice on this forum, you must be very specific as to exactly what you want a given piece of gear to do for you and at what price point. Otherwise, you will get a lot of random advice from members. Distinctly unproductive. (We all like to promote our favorite gear.) Good luck!

I am familiar with that vintage gear having sold many back in the day.
 

Currently the music room has a modern well reviewed but vintage looking NAD c3050 integrated amp available. That and chose your speakers there for a nice modern upgrade for less than $2k.  The vintage gear is neat but most good quality modern gear will slay it.  

@mapman +1! Plenty of used NAD integrated amps available on different sites: Audiogon, EBay, Reverb, USAudiomart ...

Since you have CD's a new low-cost CD player would be a good addition.

@knotscott ”Speakers often have the most impact on the system”

I agree with that.  Followed by (in this order): first stage of music (so turntable), then final stage of amplification, then preamp.

OP:

Older CD transports (1990s) are actually much better built than most current models.  (There are some exceptions.). The only things that have really improved are the DACs and that is very much an incremental change.  So that would be a last stage change, especially if you have digital out where you could use the good transport you (probably) have with a more modern DAC.

basically, start on the outside of the chain (except CD) and work in.

OP:  before giving advice, tell us about your room and listening preferences.  Those speakers, for example, might be just fine in your circumstances.  Or, for example, let’s say you have a giant space, so making full range speakers with big subs and lots of amplification might prioritize over the sources.