Ahem. Let an ol' instructor from one of the modern 'upgrades' to the Barracks (The US Army Artillery School at Fort Sill) say a few words. . .
Any upgrades should serve a specific purpose or they are wasted effort.
The modern versions of Barracks and Stable, as those buildings are used in the game, are:
Maneuver Area - like Grafenwohr, Germany for the Bavarian, German Armies, and the US Army in Europe, or the Soviet/Russian 'Poligons', or the US Army's Fort Hood, Fort Benning, Fort Leavenworth: an area big enough for mechanized units to Play War and hone their skills. Because of their size, this would in game terms, be a tile-sized District.
Artillery Range - again, these take up lots of room because modern (20th century +) artillery has long ranges. They are, therefore, frequently combined with the Maneuver Areas.
Specialized Schools. These are a combination of Colleges for officers to learn special skills related to branches like armor, artillery, and Special Warfare, and places to research new techniques, tactics, and equipment for those types of warfare and units.
Examples:
US Army's Artillery School at Fort Sill
Aberdeen Proving Grounds
Kubinka Poligon in the USSR, where, among others, the T-34 tank was tested and approved for production.
The Ranger School at Fort Benning, Georgia.
In addition, the 'regular' Military Academy of the Industrial Era has a function that the game doesn't show yet: officers trained at West Point, or Sandhurst, or St. Cyr, not only were better officers in a combat leadership sense, they were also trained military/civil Engineers. West Point, especially, provided engineers who surveyed, supervised, and built most of the American railroads, canals, and infrastructure throughout the 19th century .
Finally, there is a National or World Wonder 'military school' that is inexplicably missing from the game: since the Germans innovated it in the Industrial Era, everybody who is anybody in the military world has a General Staff Academy: the US Army Command and Staff College, the Frunze Academy in USSR/Russia, the Kriegsakademie in Germany, etc. These produce the men who lead Corps and Armies and armed forces of the State.
The Specialized Schools and the General Staff Academy are pretty much One to a Civilization. There may be multiple versions of the Maneuver Area/Artillery Range, but they take up too much room to be built everywhere.
So, here are my suggestions:
Original Encampment, Armory, Stable, Barracks, - even though the latter is mis-named, since the 'Barracks' is a 17th century CE development - remain as is.
Military Academy - at Military Science, provides current benefits plus any Military Engineer built/trained in this District can also be expended to provide 25% Production to any Wonder, District or Building.
Maneuver Area - a new tile-sized Improvement which must be built at least 1 tile away from any city center or neighborhood district, available at Tech: Steel. Any unit that spends 1 Turn in this tile gains 25% Experience. Multiple turn stays add nothing.
Branch Schools: 1 each can be built in your Civilization. Each must be built in a separate Encampment District.
Artillery School: available at Tech: Steel. Requires Barracks, Armory. Any Ranged or Siege Unit built in this District starts with 1 Promotion.
Armor/Cavalry School: available at Tech: Combustion. Requires Stable, Armory. Any Light or Heavy Mounted Unit built in this District starts with 1 Promotion
Special Warfare/Commando School: available at Tech: Synthetic Materials. Requires Barracks, Armory. Any Recon OR Melee Unit built in this District starts with 1 Promotion
And finally, because this should be kept to a minimum in the game:
Wonder:
General Staff Academy.
Available at Civic: Mobilization. Also requires that the city have an Encampment with a Military Academy.
After completion, all Melee, Recon, Light and heavy Cavalry Units may ignore Zones of Control AND Move after attacking.
This is going to make this Civ's military very, very dangerous, but it also requires a significant investment in that military before it can even be started: see, historically, Germany's Greater General Staff based on the militant Prussian state of the early 19th century.
