How does Shakespeare invite us to compare Hamlet with Laetres and Fortinbras in Act I?
It is very clear that Shakespeare intends for us to see a correlation between these three men as they are presented in Act 1. They are all about the same age and are all, in some way, dealing with the requests (stated and implied) of their father's. The most obvious connection is between Fortinbras and Hamlet. Both of these young men are going to be trying to avenge their father's deaths and restore honor to their respective kingdoms. Fortinbras's father has been dead for some time, killed in a battle against King Hamlet. Fortinbras is striking at the this time in an effort to regain the lost lands (and lost honor) for Norway. He is acting with aggressive action by hiring mercenaries for his "army" as opposed to the actual army of Norway. By the end of the Act 1, Hamlet knows the whole story of how Claudius murdered his father. The ghost of his father has told Hamlet to rid the throne of Denmark of that "adulterate beast." Hamlet swears that he will do as he has been commanded. Both of these young men are on similar missions.
Laertes doesn't get a lot of time on stage in Act 1, but we do meet him and realize that he is about the same age as Hamlet, and that he too is still going to school. A key difference is that Laertes's father is still alive. But there is still a connection to be made. In their scene together, we have another example of a father giving advice to his son -- telling how the world is and what he should do in the world. Laertes says he will do his best to honor his father's wishes. This is just like what Hamlet will say later in the act, even though the requests made of Hamlet are far weightier than those made of Laertes.
The connection of the three men becomes even more important in Act 4, when Laertes returns in a fury to exact revenge for his father's murder by Hamlet. There we clearly see how differently THREE men handle a similar situation. Shakespeare's is setting the stage for that complication in his expositions in Act 1.