You might begin your survey of literary heroes with one of the Homeric epics, the Iliad, in order to discuss two important classical Greek heroes who became models of heroic virtues in all the literature that followed.
For example, in the Iliad we have both Achilles and Hector, who eventually fight each other (Hector dies) but for different reasons. Achilles, who is almost immortal--that is, he can only be killed by a shot or strike to his heel--fights not for politics or country but for personal glory. In fairness, many warriors in the Bronze Age fought for glory and personal honor, but Achilles embodies the concept of fighting for personal success because he is never particularly concerned about who he fights and for what reason. Hector of Troy, also a typical Greek warrior who prides himself in his fighting skills, fights for his family and country. He fights the Greeks despite the fact that he knows his brother, Paris, is the dause of the war, but as a prince of Troy, it is Hector's duty tp protect his family and country. So, even though these two men exemplify the virtues their societies expected of heroes, the road by which they became heroes is very different.
Beowulf is a great example of an Anglo-Saxon hero because he can take on and defeat supernatural beings--Grendel, his mother, and the dragon--and he can, as a king should, protect his country from other groups who seek to destroy Beowulf and his people. Among other things, Anglo-Saxon kings were supposed to distribute wealth acquired in war to their loyal retainers (the thanes and earls who were loyal to the king), and Beowulf carries out this obligation throughout his kingship, thereby insuring continuing loyalty and support from the strongest fighters around him. At the end of his life, when he knows he is too old to take on the dragon that is persecuting his people, Beowulf fights the dragon alone--eventually, with the help of Wiglaf--but he tells his retainers to stay out of the fight because it is his, not their, duty. Of course, as loyal retainers, they should have come to Beowulf's aid in the final battle, but the fact is, Beowulf took the responsibility upon himself.
The central figure of the Middle English poem Sir Gawain and the Green Knight is a knight of King Arthur's Round Table who accepts the Green Knight's challenge in order to protect Arthur, and journeys for a year looking to conclude his fight with the Green Knight, a supernatural being who appears to be immortal. Like a rational human being, Sir Gawain is quite worried during his journey that he is going to be killed, but he continues the quest despite his fears because he has bound himself to carry out this task on behalf of his king, Arthur. Gawain, like heroes before him, embodies the expectations of his society.
When you look at Shakespeare's King Henry V, you will find a king who not only fights to save his country, and leads the fight from the front, but also understands how to motivate men in dire situations to fight for their country even though there are no riches involved. King Henry, unlike several previous heroes, fights--and is able to convince other men to fight--for an idea, for a common goal that is an abstract but important concept, the survival of a country. By the time of Henry V, the real world has invaded the heroic world. Henry and Hector have a lot in common.