I've been trying to research this myself. I've been trying to get translated copies of the Chu-Yen slips without success. These excavated slips are writings and records from the Han Dynasty that had detailed information on military and legal systems, educational practices, economy, and everyday life of soldiers and civilians. I can offer some information I was able to research from various other sources:

Recruitment methods and army compositions varied during different times throughout the Han Dynasty (eg. Western Han/Former Han era vs Eastern Han/Later Han era). The Han Dynasty relied on a mixture of militia armies, semi-professional armies (eg. military colonists), professional armies, and mercenaries and auxiliaries. They recruited by conscription and taking volunteers. It seems that volunteers were promised money and/or land (so rather similar to Marian era Romans in that regard). The Western Han Dynasty relied heavily on conscription to fill its militia forces (with the men being cycled out after a few years) and semi-permanent/permanent forces stationed along the frontiers. This meant that all able bodied male between 23-56 (or sometimes 20-56) were conscripted for 2 years - 1 year for training and 1 year for active duty (though I've read some writings that state active duty was 2 years, or sometimes more in various situations).

The Eastern Han gradually abolished conscription or de-emphasized it. The Eastern Han relied heavily on professional troops, semi-professional frontier troops, mercenaries, and barbarian auxiliaries. While conscription was not favored, it could still used during times of need. However, by the time of the mid or late Eastern Han era, training standards for conscripts in the safer inner provinces had deteriorated so the quality of conscripts had significantly declined (whereas the more dangerous frontier provinces had kept up with maintaining rigorous training standards). While the inner militia forces experienced decay, the semi-professionals (eg. military colonists who provided military service in exchange for land and other incentives while also farming and feeding their garrisons), professional forces, and militia forces stationed along the frontier would have kept up their rigorous training standards and maintained themselves at a good standard.

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Quotes and sources:

"Former Han maintained a universal conscription: all male subjects of the empire from the age of twenty had been required to spend two years in military service, first in local training, and then on guard at the capital, in their home commanderies, or on the frontier. Thereafter, until the age of fity six, each man remained liable for call up at the time of emergency, and there was additional training and review each year under the Commandant..."

p. 148 of Fire over Luoyang: A History of the Later Han Dynasty 23-220 AD By Rafe de Crespigny

"all able bodied males between the ages of twenty three and fifty six, or for a short period between twenty and fifty six, were required to serve in the army for two years and were liable to recall in times of emergency. Some, but not many of the men may have been able to engage and pay for substitutes to serve on their behalf. But the great majority spent one year in training and one year on duty, at the capital city, in the standing forces that kept order in the provinces, or in the frontier garrisons. While most serves as infantrymen, a few may have acted as cavalrymen in the north, or in a waterborne force in the south."

p. 479 of The Cambridge History of China: Volume 1, The Ch'in and Han Empires, 221 BC By John King Fairbank

"...general conscription system of the Qin and Western Han Dynasty was gradually abolished and replaced with the prevalence of the military recruitment system...[during the Eastern Han Dynasty] there is no longer any requirement for the applicants. Therefore, the composition of the soldiers is complicated. Most of them are mainly social idlers and unemployed people. There are also farmers, merchants, ethnic minority men, and even prisoners of death...and criminals....The main means of recruiting troops in the Eastern Han Dynasty is the lure of property."

From The Military History in Qin and Han Dynasty By Li Shi

"The Qin Dynasty...created a standing corps of professional soldiers based on conscription. The Chinese armies under the Qin and Han dynasties conquered territories in all directions..."

p. 182 of A Handbook of Military Conscription and Composition the World Over By Rita J. Simon, Mohamed Alaa Abdel-Moneim

"The Han armies were based on the system in use in the Ch'in [Qin] kingdom and empire, namely conscription. Able bodied men were enrolled at the age of thirty and were obliged to serve for one year in their local commandery." ... "That at any rate was the system in the areas near the capital;conscripts recruited in the frontier regions stayed there permanently. But we also find paid mercenaries on the frontiers."

p. 124 of A History of Chinese Civilization By Jacques Gernet

"As for the expeditionary forces of Wu Ti's time...composed of...barbarian auxiliaries, of Chinese mercenaries, and of convicts allowed to serve time in the army. After Wu Ti, there was a tendency to reduce the number of conscripted troops; the armies of the Second Han Dynasty consisted mainly of veterans, mercenaries, and very large bodies of barbarian auxillaries."

p. 124 of A History of Chinese Civilization By Jacques Gernet

Frontier garrisons and military colonies

War in Human Civilization by Azar Gat, China Between Empires by Mark Lewis, p. 420 of The Cambridge History of China: Volume 1, The Ch'in and Han Empires, 221 BC By John King Fairbank, and China Marches West: The Qing Conquest of Central Eurasia By Peter C Perdue

"the role of sanctioned militarization diminished in the Later Han Dynasty. Universal military service was abolished by Emperor Guangwu, the value of ranks of merit depreciated...the Former Han was aggressive and militarized, whereas the Later Han was defensive and civilized." ... "Ying then argues that the abolition of unviersal military service led to the failure of Later Han's military capability....the Later Han empire came to rely increasingly on foreign recruits to fill the ranks of its army along the frontier....troops under the command of Colonel Supervising the Qiang were mainly composed of the Qiang and other non-Han people, Duan Jiong's mass slaughtering of the Qiang rebels was in facted carried out by his Qiang soldiers."

From The Collapse of China's Later Han Dynasty, 25-220 CE: The The Northwest Borderlands and the Edge of Empire By Wicky W. K. Tse

"...exposed the faults of the later Han militia...With limited training in weapons or manoeuvers, troops from the inner commanderies might be used against local banditry or small scale insurgencies, but they were quite unable to cope with an emergency on the frontier....program adopted by Ren Shang, whereby potential militia men paid cash in exchange for service so that fewer but more effective troops could be raised."

p. 188 of Fire over Luoyang: A History of the Later Han Dynasty 23-220 AD By Rafe de Crespigny

"men of the inner empire might serve as local milita against bandits, and they could be called up in emergency, but they recieved no formal training or regular exercise. There was a scutage tax [gengfu], whhich contributed to the imperial revenue and supported the professional army, while the men of the frontier commanderies were liable for conscription and militia service as before."

p. 155 Imperial Warlord: A Biography of Cao Cao 155-220 AD By Rafe de Crespigny

"only in the frontier commanderies was there a regular system of compulsory service and militia training."

p. 87 of "Northern Frontier: The Policies and Strategy of the Later Han" By Rafe de Crespigny

"In 30 AD, however, among the inner commanderies of the empire the position of Commandant was removed, with all military responsibilities transferred to the Administrator, and the annual manoeuvres were discontinued. In the following year, the units of skilled soldiers...were also disbanded."

From A Biographical Dictionary of Later Han to the Three Kingdoms (23-220 AD) By Rafe de Crespigny