Personally, my reaction to Shakespeare's Hamlet, Act One, scene three, is that we are presented with a typical family situation where a father tries to provide advice to a youngster, who, in turn, tries to do the same to a younger sibling.
The brother and sister are probably the most predictable. Laertes is going away to school and his father is offering him advice to guide his actions while at the university. Laertes, not just as the older sibling, but a male (in this era) has the right to speak to his sister, who socially, has no power whatsoever within their society. However, as typical of many sisters with their brothers, she finds herself easily able to call him to task, warning him that his advice to her should be advice that he himself will heed. If it's good advice for her, it is just as sound for him.
The unusual aspect of this scene is found with the character of Polonius. He is the King's advisor, having first served Old Hamlet, and now Claudius, the dead King's brother. The part of the situation that is so ironic is that Polonius may be the King's advisor, but he's not a very intelligent man. He has excellent advice for others, but cannot seem to follow it himself. Instead, he is more motivated to make himself indispensable to Claudius, even if it means using his daughter to trap Hamlet into giving Polonius valuable information that he can then give to the King, for Polonius' personal benefit.
The one person who seems to be the most closely aligned with reality is Ophelia. Ironically, it is Ophelia who dies after she loses her mind over the death of her father, and perhaps Hamlet's abandonment of her. Polonius dies because he is sneaking around and Hamlet mistakes him for Claudius. Laertes dies because he dishonorably aligns himself with Claudius in order to kill Hamlet to avenge Polonius' death.
It would seem that although Laertes does not seem to think he needs his father's advice, following it might have saved his life. E.g., Laertes should have been more cautious: he should have kept his own counsel, hiding his thoughts, and should have been slow to act, rather than joining himself with Claudius so quickly...who uses the young man's sorrow to manipulate him to kill Hamlet.
Give thy thoughts no tongue,
Nor any unproportion'd thought his act. (I.iii.63-64)
Polonius could have benefitted from his own advice as well. Speaking to Ophelia, Polonius says that "mousetraps catch fools."
Ay, springes to catch woodcocks. (I.iii.122)
Ironically, Polonius is much like the mouse caught in a trap when he is mistakenly killed by Hamlet, even while the Prince says, "A rat! Dead for a ducat..." comparing the person he has killed behind the curtain to a vermin.
The greatest tragedy I think is for Ophelia who is the innocent in all this. Laertes plants the seed of doubt in her mind, inferring that Hamlet is not truly interested in her love but in sleeping with her, for she is beneath Hamlet's royal station and he (according to Laertes) could never marry her. Coercion by her father and the King, and doubts planted by Laertes and Hamlet set Ophelia up for destruction.
Not listening to advice brought about the destruction of Polonius and Laertes who had control of their lives but used it poorly; while following the advice and directions of the men around her bring about Ophelia's destruction, the woman who had no say in how she managed her life, but was subservient to the men and the male-dominated society of which she is a part.
This scene from Hamlet introduces the themes of deceit vs. honesty, love vs. betrayal, and reality vs. appearances. Thus, you may wish to choose one of the themes to which you wish to write a reaction. Certainly, the hypocrisy of Polonius becomes apparent in scenes that follow as he gives his son Laertes advice, as well as Ophelia, whom he also counsels.
For, as Laertes is readying himself for his voyage to France, his father, Polonius counsels him before he departs in one of the more famous Shakespearean speeches. Unfortunately, Polonius does not follow his own advice, such as
Give thy thoughts no tongue,
Nor any unproportion'd thought his act.
Be thou familiar, but by no means vulgar.(65)
For, later he prattles on so much that Gertrude must ask him to stop and make sense. He counsels Laertes to be discreet and reticent, yet in Act II he gives Reynaldo, his servant, instructions to spy upon Laertes. These actions of Polonius that contradict his words prove Polonius not only hypocritical, but rather ridiculous.