SEEKING ADVICE: Which component would you upgrade first?

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.

Man what a cool trip back to the day!  

I wouldn't sell any of that stuff. Keep it because it's your first love. 

Now, If you want to pursue HiFi get in the mindset that you'll spend about 5K to get something you'll really love and be proud of.  

Speakers come first. Spend your bucks on a good set of quality used speakers. Magnepan LRS direct from Magnepan is a fantastic honest to goodness audiophile speaker at 1,000.  Get an REL 7i sub for a grand and your have a fantastic speaker set. 

The next thing you will need to spend money on is a DAC. "Put your money in a DAC" as they say (who is they anyway?). PS Audio had  Direct Stream Perfect Wave Mark 1 that they offered $3500 for as a trade in on their Mark II.  Guess what happened? The used Mark 1s dropped to $1800 because everybody got the Mark !!.  I have both- the Mark 1 is 90% as good as the Mark2 and they are fantastic DACs  PS Audio makes sweet little streamer called the AirLens that is a steal. You will pay major dollars (up to 20K)for a fantastic Aurender but it will only be 20% better than the AirLens. 

Next stop is an amp.  I'd be all over a used Audio Research I-50 tube integrated amp. For 1K they will throw in a DAC card and a Phono stage.  Actually you could skip the external DAC above described and cruise out with the loaded I-50.  Used they are +/-4K.  

$ Value Conclusion:  ARC I-50 integrated amp with DAC and Phono card plus a set of LRS maggies and a REL 7 you have about $5500 in a kick-donkey legit HiFi system you will love for many years.  You haven't lived until you spin your favorite records while looking at the tubes glow and feeling the radiant heat from them. It's magic.