Hamlet's first words in this play are an aside that he speaks when Claudius refers to him as my "cousin and my son." Hamlet then says
To me, this shows something about him. It shows that he is an unhappy person. But, when combined with his next lines, it also shows that he is not decisive. These first words show he does not like Claudius, but he does not act that way towards the king. Instead, he denies that he is unhappy and does not let Claudius know what he is thinking.
So we see that Hamlet is someone who is going to be unhappy but will keep it to himself and brood on it rather than acting.
Hamlet's first words in the play are about his uncle and stepfather, Claudius: "a little more than kin, and less than kind." The line uses punning, for "kind" means both kind-hearted and natural, according to Shakespeare scholar David Bevington. Hamlet is here saying that his uncle is more than his uncle now, having married his mother, thus "more than" kin, and that this is less than natural. He implies it is unnatural to marry your brother's widow, which would have resonated with audiences who would have remembered that Henry VIII did that, followed some years later by a spectacular divorce. He is also saying his uncle's behavior is not benevolent or kind-hearted. He implies that his uncle did not marry Gertrude out of disinterested motives. Moreover, he states from the start that his uncle is not the kindest or most benevolent person.
We note from these first lines that Hamlet is a person given to wordplay and double entendre, one who will use words that have double meanings, which is true throughout the play. For example, he will tell Ophelia to get to a nunnery, which plays on nunnery as both a word for a convent and slang for a whorehouse. He will use words to disguise his meaning, and he will keep his thoughts to himself, so that only the audience is privy to them. He will be a mystery to those close to him.
Further, opening with these lines characterizes Hamlet as a prince obsessed with the domestic drama of his family life. This concern will continue to characterize him throughout the play.
This quote shows that even before his encounter with the ghost, Hamlet has bitter and cynical feelings about his uncle's marriage to his mother. We can assume troubles would have brewed without the intervention of the ghost.