My hunting partner is a former taxidermist and even though I have gutted, skinned and cut up my own deer for many years, when I started hunting with Wayne I learned how much I didn't know about the whole process. That guy can peel a deer quicker and cleaner than anybody I've ever seen. He showed me the RIGHT way to 'get the guts outa that critter' with the least amount of mess and fuss.
We dress the deer where they fall, get them home ASAP, hang and skin them. We let them hang for a week or so (the temps here in N. Idaho during deer season are cold enough, generally, to allow this) before cutting them up. We trim all bloodshot meat immediately, get all the goo and other stuff that doesn't look like meat from the insides, hose them out and use a small propane torch to burn all the hair off of the meat. When butchering we trim ALL of the fat and sinews and that thin membrane that sticks to some of the meat. Wayne is meticulous about cleanliness and the overall handling of game animals.
Get the guts out immediately, skin as soon as possible, get that meat trimmed, clean and hairless NOW, hang for a week (weather permitting) and you will have the best venison you ever tasted.
I'm curious as to how many of us like deer liver and heart. I love liver but don't care for heart. Back in the old days lots of guys I knew ate the brains as well, but if I don't want to step in it I don't want to eat it.