Hi there. I answered a somewhat similar question here which you might be interested in, although I do focus on Italy and using Italy as a stand-in for "Medieval Europe" is, as I elaborate in the linked answer, somewhat unsatisfying given the pervasiveness of an amalgam of English and French societies in popular conceptions of the European middle ages (even in Italy!). Other users are more than welcome to post integrative answers!

In any case, the short answer is that those called up to fight had typically already been granted some sort of privilege by whomever had the right to call them to war. Across western european cultures, systems appeared where men could be offered room and board in the household of a great lord, or have been granted their own plots of land (sometimes with renters or bondsmen to work it). What is fairly consistent is that soldiering in medieval Europe was the purview of people who had the ability to own arms, armor, and the free time to dedicate to learning how to use them. In my own area of expertise, Medieval Italy, warfare was initially delegated to an entrenched landowning aristocracy who administered a second tier of land-owing vavasours. As the governmental systems in place in Italy became more complex, by the thirteenth centuries urban professionals had become politically enfranchised and their leaders, who many times insert and integrate themselves with the nobility, created a varied and nuanced interplay between town and country: there could be members of the upper middle class like notaries, lawyers, bankers, and moneychangers owning estates outside the cities. These members of the upper middle class would also be expected to purchase and train with their own arms and armor, particularly in cities like Florence and (sort of) Venice, where the government system was heavily skewered towards the urban professionals (in other places, notably Lombardy, in spite of urbanization and similar economic development, there remained an influential warrior-aristocracy which drew its wealth from land ownership). Even the less prosperous urban professionals and artisans would eventually be expected to own arms and armor, with the crossbow a particularly favorite weapon: expensive weapons that required relatively little training, the perfect combination for prosperous urbanites, who were individuals with disposable income but, unlike the landowners, little free time on their hands.

That's not to say there were no attempts to expand the socioeconomic pool of military recruitments, in the aforementioned link I do discuss systems where Italian polities try to do just that, but even these efforts only ever involved freemen. Plus, the difficulty of mobilizing the minor guilds and/or lower middle class in Italian cities meant that when Italian hosts set out in force there could nonetheless be a disproportionate amount of crossbows, a middle-class weapon as explained above. Nor is it the case that the benefits of soldiering limited to the a-priori privileges awarded to the warrior-elite; heading off to war could result in share in the spoils of victory, ample opportunities to gather loot, and even acquire fame (important, for example, for landless fighting men hoping to be rewarded for their service with a grant of land). As time went on, professional companies of soldiers paid in hard currency would emerge, but that's a different story.