LOL this is kind of funny. I just had a class discussion on this topic last week. We were not debating the topic but merely analyzing two articles about it, one for the death penalty and one against the death penalty.
From the articles we were given I couldn't support it. Although in are class study the articles didn't give much to back up either side.
Really your question is far to generalized. I'm for it if a person has committed a serious crime such as murder and is found guilty with no doubt in the judges/jurors minds. After found guilty they should be executed. There is no point in wasting are tax dollars letting them appeal it for the next 10 years. That's where that 4.2 million cost figure is coming from you quoted above.
However if the evidence isn't 100% conclusive I'm against the death penalty. If there is any doubts about if the person really did the murder they shouldn't be executed.
If your trying to support it google Isaac Ehrlich and his studies regarding for every inmate executed 7 lives were saved.