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

I bought my system back around the same time, 1976-77 and the Altec 19s have remained quite solid for many years. I did have the driver freshened up at GPA and I did have the XOs recapped by a friend who knows electronics. Basically just new upgraded caps after over 40 years. I drive the 19s with a vintage Sansui G-9000 receiver that produces more WPC than I have ever needed but remains crisp and faithful after all these years. My TT is a Luxman PD121 set up with and external Denon AU 320 step up and denon 103 MC cartridge. I did hear my 19s through a MacIntosh tube setup once some years back and this did cause my heart to flutter but it also caused my wallet to run. Yes, if you have the $$ then do look into a good tube setup and get the XOs updated with fresh caps and that is a rather inexpensive and simple fix. One of my horn drivers dropped the tangerine phase plug when the glue dried out but this was repaired at GPA on both of the 802-8Gs. Altec 19s do like some punch if you enjoy loud music so don't skimp on power even if you buy a tube amp. All my pals who listen to my system just can't believe such great sound comes from gear that is 45+ years old.

My girlfriend has an old Onkyo receiver and JBL floor-standing speakers from the 80s.  I got a WIIM mini network receiver with optical out into a small DAC that goes into the receiver with RCA cables.  I use a streaming app from my phone into the WIIM.  

It sounds really good.

Go ahead and splurge on a Luxman SQ-N150 Tube Integrated Amplifier.  $3300 and plenty of power for your Model 19s.  Looks cool and takes up very little space!
Spend some time auditioning speaker cables, power cables, and perhaps a dedicated circuit and power conditioner (if needed).  I would look at Shunyata.  And don't forget room conditioning!
I don't know what your table/arm/cart is, but you will have plenty of $ left over to upgrade if desired.

Note:  I ran my gray box Altec VOTT A-7s with a Dynamo ST-70 (modified and upgraded with a modified PAS 3x) for years and loved it!  Nice juicy tube sound!  The Luxman is much more accurate and less "tubey", but if I had your speakers I would certainly audition it.

As @carlsbad2 said, your Altecs are ungodly efficient.  You're probably never pulling more 10 watts and mostly never more than 3 or 4.    Those speakers were designed in the days of tube amps and are quite happy with them.  I think your best bet for tube amps would be those from VTA.  You can either enjoy the immense satisfaction of building them yourself from well made kits, or you can buy them fully assembled and tested.  

As efficient as your Altecs are, the ST-70 at 35 wpc will still be overkill.  I'd run them in triode mode at 20 wpc and you'll still have more than you need.

https://tubes4hifi.com/