I feel it is time to upgrade my 1977 system.......

So 70's solid state is the pinnacle of amps?

I'd throw in a pair Atma-Sphere M-60's and a Mp-3 preamp. 

How about an Audio Research I/50 Integrated Amplifier with phono input module? Looking at a sticker price of $7250 and it has more than sufficient power to drive your Altecs. You can also add the DAC module should you want to have a digital signal access. That would leave you with approx. $10k. for other upgrades such as cables.

Another integrated amp to consider is the Western Electric 91E which cost $15k. With the next generation 300B tubes this is another excellent candidate for your upgraded system.

@glm911 First off, congrats on 46 years of musical enjoyment from your system. That's pretty amazing in itself.

You've gotten some very good advice here.  "New stuff" sounds great, and bang-for-the buck (or is that sound-for-the-buck?) pegs the needle on the cost/performance meter.

It's impossible to throw objectivity, subjectivity and emotional attachment in a blender and try to predict what's going to make you happy in the future.  I'll just throw this out there (if you head isn't spinning enough already):

IF you love the Altecs, you can make them sound better than original. While I have extensive experience in speaker upgrades, @pdreher has hands on experience and owns a pair.  Not knowing the internals of the Model 19s, I can only speak iin generic terms.  That being said, the crossovers of that era used production quality parts, cabling, connections, etc.  Those components (caps in particular) are ready for replacement.  IF the Model 19s are like many speakers the crossove boards can be pulled and shipped off for upgrades.  IF the budget allows, custom, hand-built crossovers can be built and shipped to you, complete with pigtails ready to put back in place.  As a "speaker mod'r" the goal is not to paint a mustache on the Mona Lisa, and try to make the Altecs not sound like the Altecs.  The goal is to deliver the performance the original designer would have produced if technology, time and budget were available at the time.  They will still sound like Model 19s.  Just much more transparent, focused, detailed, and musical.  Not quite a polite British loudspeaker, but something smoother that you can play louder, longer with less fatigue.  

As for the Pioneers, they are still very desirable (and valuable) pieces.  You can get a reliable "fix" if you want to make the journey to the hifi repair shop.  Or, like the Altecs, they can sound better than original.  (A Spec 1 left our shop sounding much better than it did when it came in). 

As some suggested, adding a phono stage would be signifcant sonic upgrade and take up very little shelf space.

@OP - What model is your Music Hall Turntable. If it's one of the more budget offerings, you should include a Turntable / Arm / Cardridge upgrade.

As regards amplification, a high quality integrated is more than sufficient for your speakers given their efficiency. Passlabs has been mentioned and is excellent.

I'm not sure of Copland from Denmark is distributed in the US but they make excellent integrated amps.

Prima Luna has also been mentioned and is a good choice in Tube amplification.

If you are using old cables with your system currently, be sure to put aside part of your budget for decent cables. The list is endless, but in terms of widely available cables, Audioquest do a very good job.