The Janissary is stronger than a Musketman (both in terms of raw strength and its free promotion) and can be trained twice as fast, but will reduce the training city's Population by 1 if it was originally founded by the Ottomans. To offset this penalty, the Ottomans should turn any enemy cities that they capture in wartime into Janissary training centers, then continue pushing deeper into enemy territory for as long as their resources allow.
However, since the Ottomans do not have any significant bonuses towards early conquest (except for faster and stronger siege units, which are frankly not enough without other units to back them up), the most cost efficient way to train Janissaries is to mass produce Swordsmen and upgrade them when Gunpowder is unlocked. The bottleneck of training Janissaries lies neither in their potential Population cost (as it is easy to circumvent) nor in their Production cost (as it is 50% cheaper than the standard Musketman) but in Niter availability. Since Niter is unlocked very slightly sooner than Janissaries, you have little chance to stock up this resource beforehand, while more likely than not, you have a stockpile of Iron lying around. Even after unlocking Gunpowder, as long as Swordsmen are not obsolete, train them and upgrade them into Janissaries. Due to the Janissaries' low cost, combined with Professional Army and Retinues, upgrading is cheap in terms of both Gold and Niter. By doing it this way, you can have your army of Janissaries without having to make early conquests when they are not the most favorable to you, or having to wait for Niter to start piling up so you can train Janissaries one by one and potentially missing your window of opportunity to use them.
Although it's true that the Ottoman war machine is at its peak in the Renaissance Era, it is entirely possible to engage in conquest as early as the Classical Era and gain the conquered cities needed for Janissary production. By combining Ibrahim's innate ability of +20% Production towards units and the God of the Forge pantheon's +25%, the Ottomans can gain +45% Production towards all military units in the first two eras and +95% Production towards Catapults. With Ibrahim's Serasker title, Ottoman Catapults can gain an additional +10 Combat Strength bonus (which, in conjunction with the +5 from the Ottomans' Great Turkish Bombard ability, gives them a total Combat Strength bonus of +15) when attacking districts, allowing them to destroy the defenses of even walled cities in the blink of an eye. This is especially effective against neighbors that play defensively and have potential to snowball if left alone, such as Korea, China, or Greece when led by Pericles.
The elite infantry of the Ottoman Empire had a lasting cultural impact within the Ottoman Empire and on the military history of the world at large. The Janissaries embodied many aspects of the Ottoman Empire's systems of governance and warfare, and remain one of the most recognizable military forces in history. At the time they were created in the reign of Murad I, they were a revolutionary military force (the term Janissary literally means “New Soldier”) combining iron discipline, strong esprit de corps, and the latest military weapons.
The Ottoman Sultans were entitled to extract a fifth of the value of their territory. Often this took the form of levies of labor or manpower. Christian communities in the Balkans were compelled to provide boys to the Janissaries. The boys were taken from their families and communities, converted to Islam, and then raised in the strict discipline of the Janissary corps.
Janissaries were originally forbidden to marry (this stricture was relaxed later) or engage in trade, and swore loyalty to the Sultan himself. The Janissaries had their own distinctive marching bands—the mehter—which influenced European military marches in successive centuries. They were well-paid, and given the special attention of the Sultan, who would appear once a year among his Janissaries to draw his pay. The Janissary corps was strongly meritocratic, and a successful Janissary could retire with a pension and considerable cultural prestige. The Janissaries may have been the first infantry force to be predominately equipped with muskets. They wore uniforms at a time when the practice was still uncommon, with a distinctive high white hat with trailing flap.
The Janissaries became one of the most politically-powerful factions within the Ottoman Empire and comparisons to the Praetorian Guard of Rome are apt. However, they resisted most of the efforts to reform their organization, bringing them into conflict with later Sultans. In 1826, the Janissary corps mutinied in response to European-style infantry reforms. Sultan Mahmud II turned cannons on their barracks and executed any Janissary who survived the bombardment. This event was termed the “Auspicious Incident.”
The Janissaries were pivotal to the military power and successes of the Ottoman Empire, and they influenced the development of musket armies in Europe during the transition to the age of gunpowder. Their organization and history provides insight into the organization of the Ottoman world. Even their enemies respected their discipline and admired their panache.