All right. Abusing my mod powers, I can see that the attempted answers to this question are basically dumbed-down lists of "possible careers in the Middle Ages": priest, monk, knight, soldier, artisan. Besides being woefully incomplete overall and in some cases impossible, that list fails to address the core of the question: (a) how does being an eldest son affect choice of future (b) how does being a serf affect choice of future (c) did medieval peasants/serfs even have the concept of "choice of future."

To the last, the answer is definitely yes. Simon de Paris ("de Paris" is a surname in this case; French 'le' and 'de' were common in late medieval English surnames) became sheriff of London (!) in 1302. But he had originally been born a serf in Necton!

De Paris had taken advantage of a provision in London law, like many cities, that a serf resident in the city for "a year and a day" would be considered legally a freeman as long as they were within city boundaries. He had gone further, though, making enough money as a textile dealer to purchase a London citizenship. Presumably, he'd come from a better-off serf family in order to get established as a mercer.

So as the case of de Paris also indicates, one thing to do was to just up and leave one's probably not so huge...tract of land and hope they didn't get caught. (We know about de Paris in large part because his original lord tried to claim rights over him. De Paris was powerful and rich enough not just to keep his freedom but to win a legal settlement against the lord afterwards.)

However, he is very, VERY exceptional in his wealth. Most serfs--most peasants, period--who immigrated to cities almost certainly ended up as servants or petty laborers, not full shop-owning artisans and definitely not merchants.

The next thing to consider is that farming was absolutely not the only occupation of peasants, including serfs. It's true that serfs and tenants typically owed the lord X number of days of labor and rent/tithe in kind or in cash, and that typically those payments involved agriculture. But not always! Some areas were heavily pastoral (herding), and even ones that weren't still needed herdsmen. Other possibilities were mining, especially coal (although in Germany, miners were typically freemen), or timber-gathering in forested lands.

And even serfs who did perform field labor for their lords were not limited to farming in their daily lives. Medieval villages still needed petty artisans--blacksmiths, carpenters, brewers/brewsters--who might be full-time or part-time.

As to the final issue, the "eldest son" part: primogeniture was not the law everywhere and everywhen in the Middle Ages! Some English areas even practices ultimogeniture--last son inherits--others had rules about splitting inheritance. But often things were more freeform. So being the oldest son, one might be more expected to take over the bulk of family land and responsibilities, and perhaps be socialized to want it more. But resistance was possible.

There are very, very many ways it was terrible to be a serf. But medieval serfdom was still not what we think of as slavery, with the complete lack of control that enslavement brought.