A prince would be raised to be skilled in the arts of warfare, he would learn the use of weapons, and to ride, hunt, and hawk. He would be expected to take an interest in the businesss of government, as one day he might have to rule. The oldest son of a king would be the most important, as he would be next in line for the succession, but life was uncertain in medieval times,a prince might die of disease, or in battle, in which case the next brother in age would be king (unless the oldest son already had a son of his own when he died). Princes would have their own estates and castles. He would be expected to take an interest in the running of his estate, the crops being grown, welfare of his tenants etc.
Piety was an important quality for a prince, he would be expected to go to Mass, and pray every day.
If there were several sons jostling for positions of importance, it would cause problems for the king. This occured for instance with King Henry II of England, who had a lot of trouble with his sons. He made his oldest son, Henry, king of england while he was still alive, but this did not satisfy young Henry or his brothers, and they eventually rebelled against their father. The rebellion was crushed.
A prince would have many servants. Since he would normally have his own household, he would have all the servants that went with a royal household, a steward, a chamberlain, a chaplain, many waiting servants, cooks and scullions in the kitchen, grooms out in the stables. And men at arms to guard the place. There would be a huntsman to take care of his hunting dogs, and a falconer to look after the falcons and hawks (hunting was a major occupation of royalty and nobility, it was not just for sport, but provided much food for the table).
Life in a Medieval Castle by Frances and Joseph Gies