Short answers, pulled from the story.
King Servius Tullius instituted a universal levy of eligible adult male citizens in 550 BC. This development coincided with the introduction of heavy armour for most infantrymen and established a standard levy of 9,000 men.
Service in legions was limited to property-owning Roman citizens aged 16 to 46 years old. Conscripts served only for each campaigning season and disbanded thereafter without maintaining standing professional forces.
By the end of Augustus reign the imperial army numbered some 250,000 men equally split between legionaries and auxiliaries. Numbers grew to peak of about 450,000 by 211 containing 33 legions and c. 400 auxiliary regiments.
Emperor Diocletian took power in 284 initiating significant transformation of the Principate army structure. The army of 4th century heavily depended on conscription and soldiers were more poorly remunerated than in 2nd century.
The last decisive battle fought by the Palaiologan army occurred on the 29th of May 1453 when Constantinople was besieged and fell. Last isolated remnants of the Byzantine state were conquered by 1461.