Hamlet and Regret/Redemption (or lack thereof)

One particular aspect of Hamlet I find interesting is the coupling of vengeance with regret. Hamlet is obviously built up as the protagonist and he seeks vengeance for his father. However, his uncle, against who whom he seeks vengeance, doesn't seem particularly bad. He is seems to be an acceptable King, which Hamlet's father might not have been; he is in purgatory, which can mean he lived a moderately sinful life that wasn't good enough for him to go to heaven (though it's possible his presence in purgatory is the result of his unfinished business on earth, it is described as a fiery purgatory in which his sins are burned away). Claudius wants redemption for his sins, which is why he tries to pray in Act 3. The fact that he fails at praying and thus doesn't feel redeemed is also interesting because it reflects the lack of redemption he receives from the audience, who always side with Hamlet. This is despite the fact that Hamlet also kills people (Polonious and indirectly Ophelia so far).