SEEKING ADVICE: Which component would you upgrade first?

Speakers often have the most impact on the system. Find something you love that works well in your room, and that can be driven by your amp.  Lots of great deals on used speakers in most markets. 

A cart upgrade is a never a bad idea! 😎

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.