Like Hamlet, I would have some serious qualms about taking a life, and can with almost 100% certitude say I couldn't kill Claudius. I actually think I would be afraid to do anything -- after all, if he killed once he could kill again! I guess I would always be on the look-out for evidence that I could take to the authorities, but I would be VERY stealth about what I knew.
I don't think that revenge in the revenge tragedy sense of the expression is something that I could do. Of course, we have to recognise what a difficult position Hamlet is in. He has no escape and the situation is so messy and complex. Certainly this might help us understand why he dithers and procrastinates so much. I guess I would want to try and bring Claudius to justice and not hurt others in the mean time, but how likely such a choice would be is difficult to say.
If I were in Hamlet's shoes, feelings of helplessness would completely overwhelm me. I can relate to Hamlet most when he thinks of Claudius enjoying the fruits of his crime and crying, "Smile and smile and be a villain." The fact that Hamlet's mother is married to the culprit only compounds matters. Even though I would long to exact revenge, I don't think it would be within me to kill another. I would be launched into a very deep depression. My trust in people would evaporate, and I would just want to leave. Of course, Hamlet is denied even the chance to leave home.
I'm no saint, but taking personal revenge is not something I think I would do. Of course, thankfully I haven't had anything happen to people I love as Hamlet did; if I did, my answer might be different. As it stands, though, the closest I would get to getting revenge would be to gather, with a vengeance, evidence of guilt. It would be my greatest pleasure to see the murderer punished; however, I don't see it as my role to do the punishing. I'd like to think those feelings would transcend time and place--but I'm just not sure.
The answer to this question varies with the one who answers. In the real world of today, the smartest course would be to try to find concrete evidence and go to the police, or at least, without divulging the ghostly visit, try to get the police to investigate Claudius. But the play cannot really be removed from the time in which it is set. There was no forensic evidence or autopsy in those days. Today the cause of death would be known very quickly and the story of King Hamlet being bitten by a serpent would not hold water (Act 1, sc. 5, ll 36-38). Investigators today know to first look at who has the most to gain in solving murders and certainly Claudius, having received the throne and then quickly marrying Gertrude would be the prime suspect. Claudius would probably crumble before long under lengthy questioning and spill his thoughts just like he does in Act 3, sc. 3 when he is praying in the chapel after seeing the play and reacting. The best revenge is to triumph and if the matter of Claudius' guilt were turned over to the proper authorities to investigate and then turned over to the courts for prosecuting with all the public scandal it would cause, the revenge would be sweet. A revenge of violence against Claudius may play out quite well in the movie theaters but in real life, it's just another criminal act.
The first question I would address would be whether revenge is an appropriate act at all. This is not an inconsequential step, in that it is the one that Hamlet is stuck on throughout most of the play. And, because Shakespeare emphasizes the point of deciding to act rather than the carrying out of the act itself, we should not jump ahead of this when considering revenge in relationship to the play.
Revenge Tragedies were very popular in Shakespeare's day, the most famous probably being Kyd's The Spanish Tragedy. In most Revenge Tragedies, the suspense of the play came from how and when the main character would carry out his revenge, not whether he would actually proceed with the revenge or not. Hamlet considers many aspects of this question of revenge, making this play one in a completely different league than the standard Revenge Tragedy.
For myself, I would also consider revenge first, before deciding what to do "to achieve revenge." And, since I believe that, basically, "two wrongs don't make a right," I would stop at the point of consideration, no matter how wrong I felt that action that could potentially be revenged might be.
I've provided some links below for more information on Revenge Tragedy and an essay about Hamlet's delay in enacting his revenge.
It would depend on if I had any more information than Hamlet or if I am occupying his exact position to see if I would do the same things as he would have done. IF not I would have gotten revenge in a more simplified way. While in his place, I would have have requested that performers perform the play within a play scenes.