Grant is a perfect example, a drunkard...but by God the man could fight!
He was a mediocre president later on but it is for his actions as a general that I include him as a flawed but extraordinary gentleman.
Franklin schemed to make money from everything he was involved in from the post office to printing the currency. He was loyal to the crown until it became clear he must become a patriot. And he loved the ladies. :-) He would have served as president but was simply too old by the nations founding. His worthwhile accomplishments are legion.
Churchill flipped back and forth between liberal and conservative parties, was partly responsible for some huge military blunders (Gallipoli for one) and drank like a fish. But the man was almost singularly responsible for saving the world from Naziism.
He handled it. He was a heavy drinker but so be it. He handled it.
I commend all four of your choices, but I would have selected General Thomas Jonathan “Stonewall” Jackson instead of Gen. Grant.
http://www.civilwarphotos.net/files/csos.htm