A constitution is a statement of the basic principles and laws of a nation, state, or group, such as the U.S. Constitution. Another very common meaning of constitution is the physical makeup of a person. So think of a constitution as how a body (yours, the government's) is set up. If you have a strong constitution, it means you don't get sick very often.
I think the focus of the story is on Beowulf as a hero rather than a king because it is his heroic deeds that lead to him being offered the throne. Also to be king one must possess some type of heroic qualities in order to rule a land and its people.
There are, as you can see from the answers below, many reasons to study Beowulf. It is worth remembering that Beowulf is a work of art, not an historical document and it should be studied as such (as Tolkein most effectively pointed out in his essay The Monsters and The Critics, well worth a read).