RE: What do you do?
Well one must determine what he or she is wanting to do with the rack. If a shoulder mount you must stop at the brisket and reach up inside the deer to field dress. I also like to skin the deer in two pieces when keeping the cape for shoulder mounts, basically from the brisket a straight line around the body to create two portions. I cape out the back half first normally with little attention paid to cape knicks, etc. I then move to the front half and start with a dorsal cut(this is in the hide only not the meat!!)up the back bone to just shy of the neck. I then work verycarefully making sure to watch the knicks in cape, etc from the mid point up, lots of pulling and light knife pressure. If warm i have also done it where I remove the lower legs at the knee joint then basically release the hide by pulling and cutting without the dorsal cut...though it takesmore time and it must be pretty fresh or warm still to work reliably. Once you get to the neck area I reccomend cutting around the neck meat vs fleshing the face for those who are not real experienced. Once the neck is cut via knife around itthen just twist the headby the antlers to release the head from the carcass. Lay it out then neatly fold it and freeze or get it to the taxidermist for fleshing,etc asap. They will charge a little more but it is well worth it and will be cheaper,easier/faster and look better than having them get you a cape from a different deer. If your wanting a skull plate or euro antler only mountthen none of this is required, just cape down in 1 piece as per normal and release the neck from the carcass. Either flesh out the skull for euro or take a saw cut straight back just above the eyebrow line and straight down behind the antlers to the previous line. Remove all the hide, flesh and meat as soon as possible. Both will need to be bleached by soaking or boiling prior to mounting to a plaque or wall.
As far as the animal care after the shot. To me it is Field dressed (guts out) immediately, skinned asap, light rinse with cool water, pelvic bone split and hung via gambrel head down. I believe it is essential to cool the carcass down completely so I skin immediately and hang. If too warm I 1/4 and place in a fridge once it core temp drops. If you are taking it a locker or butcher for processing do so as soon as possible. I remove the tenderloins immediately. I only let my deer hang for 24-48hours to allow the rigor mortiseprocess(lactic acid turning back to sugar)to take place before cut and wrap.
Hope it helps you some and good luck!!