The theme or moral of beowulfs fight with grendel is Beowulf is an epic that came out of a warrior culture and was used not solely to entertain but also to teach the values of this culture.  The Anglo-Saxons valued bravery, heroism, strength, loyalty, fame through glorious deeds, and the desire to fight evil.  Their leaders were their best warriors.  Beowulf himself embodies all of these qualities, and you can find examples of these throughout the text.  He is the strongest and best warrior in his country, and after he defeats Grendel and his mother (among other victories) he becomes king.  Wiglaf, who becomes Beowulf's successor, also embodies these traits.  When all of the other soldiers abandon Beowulf in his fatal battle against the dragon, Wiglaf does not.  He displays courage and loyalty in helping Beowulf defeat the dragon, which is why he is named the next leader.  It is true that Beowulf fights these monsters to help his tribe and the Danes, but he also does so for fame and glory and hopes to be remembered for such deeds, which is why, on his deathbed, he requests that a monument be erected to remember him and how great he was.  In seeing this monument, future generations will remember Beowulf and the qualities he embodied, reminding them to fight evil forces with courage and strength and to always be loyal.  Anglo Saxon culture did not value humility.

Another interesting aspect to note is the idea of Christianity.  By the time Beowulf became a written text and not just an oral story, Christianity had begun to spread through Britain.  As such, certain Christian ideals and language are sprinkled throughout the text we read.  The most significant Christian value in this text is the connection between God and good.  When battles against evil are won, the characters praise God and rely on him to help.  However, the idea of faith is at odds with the pagan concept of fate, which is often associated with unfavorable conditions and results in the text.

So, to simply answer your question, a moral person in Beowulf is one who bravely and courageously fights evil for the sake of his people (and others) and for fame, someone who strives to be strong and is loyal to his leaders/followers; increasingly, over time, this morality also began to include a faith in God's help to win battles against evil.