Depends
I have moved Barracks around depending on my current needs ( see notes ).
Barracks has unlimited storage for troops, and leveling troops is instantaneous. So it is never has a wait timer.
Unlike Lodge ( harpoons to use excess iron ), Lab ( shards → emblems )and Academy ( mysterious Hero formations ), all buildings that have wait timers.
So I will likely continue to treat Barracks that way and build Lodge, Lab and Academy on 3x forges.
Lodge
I love harpoons ( see notes ).
But my favorite part of crafting harpoons is 7x 1* ingredients ( 5x Common Herb, 1x Large bone, 1x Clean cloth ) which is very easy to farm, and stockpile, but gives me a 5* battle item.
My second favorite part of crafting harpoons is crafting them to use excess iron. Especially since Stronghold 21- 25 were added, the build times are so long, even when I still had a second builder, iron was often wasted.
Notes
Click for notes
Barracks
Currently a level 20 Farm.
Harpoons
VIP pass
If you are only getting the VIP Pass for the second builder, I recommend buying the 30 day option.
Before my most recent uninstall of Empires, my favorite part of VIP Pass was 90x monthly loot tickets that I used for Atlantis Rising and 900x monthly gems for buying more hero roster slots. With merciless RNG, I hoard many 4* / all 5* heroes.
FIN