What type of father is Polonius in "Hamlet"?
I'm not so sure that Polonius was such a good father. He relates to his two children, Laertes and Ophelia, the same way he does with everyone else: he doesn't do a lot of thinking, is not very deep but is stubbornly opinionated, and he talks far more than he listens.
Everyone knows that Polonius is a doddering, garrulous, self-aggrandizing old fool. Just the kind of advisor a snake like Claudius would want: someone who is weak minded and easily used and manipulated. If he were a different kind of person to his children, fine, but he isn't.
When we see him with Laertes, who is about to go back to school, he gives Laertes a long, obvious, cliche-filled speech, replete with maxims that the learned Laertes must have heard a hundred times before. As he pontificates, Laertes listens dutifully, for he has already learned there would be no use in talking anyway. It's not that Polonius doesn't care for Laertes; it's just that he's all surface and no depth. The things he says to Laertes could be said to anyone.
And it's not that he doesn't care for Ophelia, but his advice to her in regards to Hamlet is insensitive and short-sighted. Worse still, he uses Ophelia to spy on Hamlet, which puts her in a difficult and painfully duplicitous situation.
As a father, Polonius does a perfunctory job, but he is not deeply caring and truly loving. If he were, he would do far more listening and advising than talking and directing. For, in the end, one can't be a better father than one is a person.
I think Polonius means well as a father, but at times he is a little bit trite and ridiculous (which probably applies to me when I'm parenting, too...).
I think that Polonius shows that he really cares about his kids when he is talking about Hamlet to Ophelia. He is warning her that a prince like that can't really just marry a girl for love. This means that she needs to watch out because Hamlet is probably just trying to use her. In that case, Polonius clearly cares about his daughter's happiness.
He sounds a bit more trite when he is talking to Laertes before Laertes leaves home. He tells him stuff like "to thine own self be true" -- stuff that's fairly obvious.
So, as a parent, Polonius seems pretty realistic -- he means well, cares about his kids, but gives pretty obvious advice at times.
It could definitely be argued that Polonius is a good father even by today's standards because he really cared about Ophelia in a time where most fathers barely acknowledged their daughters and considered them to have little worth past chattel to be given to someone as a wife or to the Church as a nun. He did his best to protect Ophelia from the harms of the outside world and genuinely loved her and did his best to protect her. He was also a good father to Laertes, letting him go out in the world to find his own way and seemed to love and care for Laertes as much as he did for Ophelia.