I did these tests today to find out which is the fastest building unit, this is what I found.
Academy-Hop-Phal-Cent-36 seconds
Archery Range-Bowmen-30 seconds
-improved-comp-30 seconds
-chariot archer-40 seconds
-elephant archer-50 seconds
-horse-heavy hors-40 seconds
Barracks-Clubmen-Axeman-26 seconds
-short sword-broad sword-long sword-legion-26 seconds
-slinger-24 seconds
Seige Workshop-stone thrower-catapult-heavy cat-1 minute
-ballista-helipolis-50 seconds
Stable-scout-30 seconds
-cahriot-scythe-40 seconds
-war elephant-armoured elephant-50 seconds
-camel-30 seconds
-cavarly-heavy cav-cataphracts-40 seconds
Temple-priest-50 seconds
Town Centre-villager-20 seconds
Well their the facts so if you want to know the quickest built army their it is.