What kind of a King is Claudius in Hamlet? What evidence shows the kind of monarch he is and the kind of man he is?

Claudius is a king who appears to most of his public as an able king, appointed and approved of by the counsel, who does his job efficently.  In the opening of scene 2 of Act 1, Claudius tells his audience that his marriage to Gertrude so soon after his brother's, and her husband's, death is justified and accepted.  He does not dwell on the matter, but moves on quickly to the matter of Fortinbras of Norway who wants to reclaim land lost by his father to old king Hamlet.  Claudius dispatches two representatives to talk with the current king of Norway to stave off any attack.  This makes Claudius appear to be a good king who takes care of problems.  Before the end of the first act, however, we learn from the ghost of Hamlet's father how deceitful, ambitious, and amoral Claudius really is.  If there was any doubt about Claudius' guilt in the murder of his brother, we have Claudius prayer-confession in Act 3, sc. 3.  Then, in Act 4, sc. 7, we also see the conniving quality that Claudius possesses when he talks with Laertes.  Claudius' plan to have the English kill Hamlet fell through, so he has a new plan for Hamlet and Laertes to engage in sword play just for sport, but for Laertes to have a sharpened tip so he can kill Hamlet.  Claudius seems like he doesn't want to get his hands dirty with murder, except in the case of his brother's murder.  Claudius is shown then to be cowardly and to be an overly-ambitious, and unwise leader and man.  He took the word of Fortinbras as it was given to Norway's king, that Fortinbras wouldn't attack Denmark, but Fortinbras did enter the kingdom.  It's clear that there was little if any Danish resistance because Fortinbras seems to easily walk into the kingdom and into Elsinore.